The Wales star has been linked with a move to Old Trafford for years and talk of an exit from Real Madrid has intensified since Zinedine Zidane’s reappointment last week.
Bale’s agent Jonathan Barnett has repeatedly stated Bale’s intention to remain at the Bernabeu, but United are one of just a handful of clubs with the wherewithal to acquire the forward.
Former manager Jose Mourinho made no secret of his desire to bring the 29-year-old to United, but caretaker boss Solskjaer was coy about a potential summer move.
“I can’t really comment on Gareth Bale or specific names because they’re property of other clubs,” the interim United manager said.
“But we should look for quality players, definitely, and players who could improve us as a team.
“There’s so many factors you need to think about when you sign players.
“It’s not easy – I don’t know if it’s easy either – when you’re in the media or when you’re a supporter, you can think short-term.
“We’ve got to think about the longevity as well, who’s going to fit in personality-wise.
“So, there’s so many things that we need to think about.”
Bale has been at Real Madrid since 2013 and is a four-time winner of the Champions League, although there is no chance of a fifth this term after bowing out to Ajax in the round of 16.
United’s hopes of European glory remain alive after overcoming Paris Saint-Germain and, speaking before being drawn against Barcelona, Solskjaer said they have proved that “on any given day we can beat a top team.”
“The confidence in the players, it’s sky high,” he said. “And the mood is good, the training attitude is good, so hopefully we can keep that run going.
“There have been a couple of comments about ‘you used to have number 20′ and it is 20 years since the treble’ and blah, blah, blah.
“I believe that you get what you deserve in life, in sports.
“If you put the work in, I believe, if you work hard, show the right attitude, if you go in every single day and do the right things you can maximise your chances.”
Before that comes a key FA Cup quarter-final at Wolves on Saturday evening – a match Romelu Lukaku could join the likes of Alexis Sanchez, Ashley Young and Juan Mata in missing.
United are looking to bounce back from their first domestic defeat under Solskjaer last weekend at Arsenal – a side they overcame in the fourth round of the FA Cup.
There have also been wins at Chelsea, Tottenham and PSG in recent months, so the suggestion that Solskjaer has got lucky has naturally worn thin.
“I think I’ve answered that question quite well here,” he said with a smile. “I think you earn your luck, but sometimes it’s better to be lucky than good, eh?
“Any game you lose is a big anti-climax. It’s the worst feeling you can have.
“And that’s maybe the only good thing about that Arsenal defeat, to feel how much it hurt.
“Because PSG we still had a chance to correct it and before then the last game I lost was against Ranheim on 26th August, so it was a long time ago.”
Former Manchester United midfielder Paul Scholes has left his role as Oldham manager after just 31 days over claims of broken promises.
It was a lengthy process to get the ex-England international through the door, with the 44-year-old last month signing an 18-month contract to kick-off his managerial career at his boyhood club.
Scholes got off to a dream start by overseeing a 4-1 win against Yeovil, but things went awry as Oldham drew three and lost three of their subsequent six Sky Bet League Two games.
Tuesday’s 2-0 loss at Lincoln proved to be his final match at the helm, with Scholes announcing his shock departure on Thursday afternoon.
“It is with great regret that I have decided to leave the club with immediate effect,” Scholes said in a statement released to Press Association Sport.
“I hoped to at the very least, see out my initial term of 18 months as the manager of a club I’ve supported all my life. The fans, players, my friends and family all knew how proud and excited I was to take this role.
“In the short period since I took on the role it unfortunately became clear that I would not be able to operate as I intended and was led to believe prior to taking on the role.
“I wish the fans, the players and the staff – who have been tremendous – all the best for the rest of the season and will continue to watch and support the club as a fan.”
Scholes’ departing statement appears to fly in the face of owner Abdallah Lemsagam saying upon his appointment in February that “Paul will have my backing 100 per cent”.
The timing of the announcement also seemed to blindside Oldham, who tweeted about their players heading away on international duty just minutes after news of his exit broke.
The club belatedly confirmed Scholes’ exit 40 minutes after it became public knowledge.
The club said in a statement: “Oldham Athletic football Club can confirm that Paul Scholes has resigned from his position as first-team manager with immediate effect.
“We would like to place on record our thanks to Paul for his efforts during his spell in charge of the club and would like to wish him well for the future.
“An update on the permanent replacement will be made as soon as possible.”
Scholes, who spent his entire playing career with United and won 20 major trophies, including 11 Premier League titles, leaves with Oldham 14th in the League Two standings and nine points off the play-offs ahead of Tranmere’s visit on Saturday.
Scholes has been working as a pundit for BT Sport in recent years and was part of the takeover of Salford City in 2014 with his old ‘Class of 92’ team-mates at United.
Salford announced before the 44-year-old’s appointment at Oldham that he would resign as a club director but retain his 10 per cent stake in the club.
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Manchester United winger Anthony Martial is in line for his first France cap in a year after being selected in Didier Deschamps’ squad for the opening Euro 2020 qualifiers.
The 23-year-old missed the cut for last summer’s victorious World Cup campaign and had to fight for his United place under former manager Jose Mourinho, but re-established himself with a run of six goals in five league games in October and November.
He was named in the original squad for November’s internationals against Holland and Uruguay but pulled out due to injury, meaning the qualifiers against Moldova and Iceland this month mark his first opportunity to feature for his country since last March’s win over Russia.
Ousmane Dembele has been ruled out after suffering a hamstring injury in Barcelona’s Champions League win over Lyon.
The 21-year-old winger scored Barca’s final goal in a 5-1 win after coming on as a substitute for the final 20 minutes, but suffered the injury along the way and faces at least three weeks out.
A club statement on Thursday announced: “Ousmane Dembele has undergone tests with the FC Barcelona medical services on Thursday morning and it has been confirmed that he has torn the femoral biceps muscle in his left hamstring. This means he will be out of action for an expected three or four weeks.”
Lyon full-back Ferland Mendy is also absent after being injured in the same game. Mendy had been expected to feature after making his debut in November’s friendly win over Uruguay.
Everton defender Kurt Zouma has been selected after winning his third cap in October’s friendly against Iceland, with Manchester City’s Aymeric Laporte left out.
The squad also featured recalls for Bayern Munich forward Kingsley Coman and Paris Saint-Germain defender Layvin Kurzawa for the first time since November 2017.
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