The 24-year-old has emerged as a potential replacement should Paul Pogba depart Old Trafford this summer.
There were widespread reports in Italy suggesting a switch was close to completion with a £90 million offer said to be on the table.
Lazio head coach Simone Inzaghi has made his stance clear on the Serbia international, he would like him to remain in Rome but understands some offers are too good to turn down.
“My thoughts are that I’d like Milinkovic-Savic to stay,” Inzaghi said. “But I also believe the club has to consider offers when they come in and then make a decision.
“Milinkovic is 24 years old now, he’s no longer a kid. I can give him advice, he is at our disposal and hasn’t missed a training session, but then I don’t know what will happen.
“I hope he stays.”
Milinkovic-Savic was touted as the ‘€100m man’ last summer and he was expected to make a move to United then, only for the transfer to fall through.
He stayed in Serie A where his form tailed off, but the physically-imposing midfielder remains a wanted man and Inzaghi is aware of the task at hand in attempting to replace such a talent.
“We know that if he was to leave, we’d have some important shoes to fill,” Inzaghi added.
“I hope he remains, he had a great pre-season training camp, but the market is open, and we are ready for any situation.
“If he were to leave, we’d need a physical player to come in the midfield. Purchases are targeted and chosen together with the club, we have sat down and talked calmly.
“If an important offer arrives, it is only right the club take it into consideration.”
Manchester United’s Eric Bailly left the Hongkou Stadium on crutches and with his left leg heavily supported after being stretchered off with a knee injury, minutes after coming on as a second half substitute during his side’s 2-1 victory over Tottenham Hotspur in the International Champions Cup on Wednesday.
United manager Ole Gunnar Solskjaer said the knee injury ‘doesn’t look great’, which raises questions whether Bailly will be fit for the start of the English Premier League season.
The defender will have a scan when the team return to Manchester.
This injury does also increase speculation surrounding Harry Maguire – United have been tracking the centre back for months after Maguire apparently told his club Leicester City he wants a new challenge.
Eric Bailly will have a knee injury assessed upon Manchester United‘s return home after Ole Gunnar Solskjaer’s side ended their tour of Australia and Asia with a win against Tottenham.
Three years after their Beijing friendly against Manchester City was cancelled, the Red Devils finally stepped out on Chinese soil once again.
Anthony Martial saw his first-half opener cancelled out by Spurs’ Lucas Moura in sweltering Shanghai, where Angel Gomes sealed a 2-1 victory as United returned home with four wins from as many games.
It was a largely positive and productive tour, but it ended with Bailly getting injured 11 minutes after his half-time introduction.
The centre-back, who missed the end of last season due to medial ligament damage, left the field on a stretcher and looked in some distress.
United boss Solskjaer said: “It’s never nice when you get an injury.
“It’s not worth it when you lose one. He’s done his knee but we’re not sure how bad it so of course we need to get back to Manchester and do the scans. Let’s just hope for the best.
“We’ve had six centre-backs rotating here and they’ve all done well.
“Phil (Jones) has played the first three games, it was his turn (to be rested) today.
“I thought Marcos (Rojo) and Chris (Smalling) really took their chance, played well first half. We looked very assured at the back.
“So, of course, you’re never happy when you get injuries. Let’s hope it’s not too bad for Eric.”
United were perhaps fortunate not to have a worse injury list after a friendly that at times was anything but, with Dele Alli, Moussa Sissoko and Andreas Pereira all guilty of poor first-half challenges.
“It’s a competitive sport and we’re preparing for the league and that’s why we have referees,” Solskjaer said.
“I thought it was a very good preparation for getting ready for the league. No tippy-toey football. You went in to tackle when you’re supposed to tackle, so I have no qualms about some of the tackles.
“Yeah, you’re worried but there’s no injuries… we also gave, we didn’t’ just receive. I thought it was a very good game.”
Sissoko’s challenge on Daniel James looked particularly bad and led to a melee in the corner.
The summer signing has been subject to rough tackling in every game during the tour but has dusted himself down well.
“Of course we want them to be looked after – but it’s also a man’s sport,” Solskjaer said. “We can’t lose tackling in football. As long as you tackle fairly.
“Dan is so quick and it’s not easy to time tackles and challenges against him, so I can understand why players mistime their tackles against him.
“He’s a brave little boy and he jumps. He’s taken a few knocks over the tour but as an old man I like to see tackles in the game.
“He gets up. There’s no rolling about, or diving or anything like this. If he stays down, he’s injured. But he gets up when he’s just hurt. There’s a difference between being hurt and injured.”