The two sides will meet in a high-stakes clash at Old Trafford, with City locked in a tight Premier League title race with Liverpool and United scrapping to get into the top four.
City have previously been accused of ‘tactical fouling’ to prevent counter-attacks when they are pressing high up the pitch, and Solskjaer expects to see that on Wednesday.
“We have got to be ready for the press and the quality they have got on the ball,” he said.
“When we win it we have got to be ready for their aggression because they will snap at your ankles and heels and kick you.
“They will not allow us easy counter-attacking. There will be fouls, no doubt about it.”
United go into the match on the back of a humbling 4-0 loss at Everton on Sunday, a sixth defeat in eight which led to questions over whether Solskjaer is indeed the right man for the Old Trafford job.
The Norwegian won 14 of 19 games while in a caretaker role, but has overseen four defeats in six since taking the job permanently.
Asked if he could turn it around, Solskjaer said: “I would like to to say yes. It’s not down to me to say that but I’m confident in my team and I’m ready to take on the challenge.
“I know it’s a big challenge, that’s why I came in when I came in.”
A big summer of rebuilding awaits but Solskjaer said he could be trusted to make the right calls on United players.
“I would like to think so,” he said. “I like all these boys. I love them. They are great lads. I have to manage for the club. I help the players but I manage for the club. I am putting all my efforts into doing what is right for the club.”
Solskjaer had questioned his players’ attitudes immediately after Sunday’s game but adopted a more balanced tone on Tuesday.
“Now is not the time to be making wholesale changes in the squad,” he said. “We’ve been doing great. Only City and Liverpool have taken more points than us in the last 18 games and that’s a great effort by the boys.
“We were where we were when we came in and we’ve given it a real go. You see lots of the Manchester United standards and DNA in many of these players.
“But we will have to get some in and some will have to go out.”
Given the problems exposed at Goodison Park, Solskjaer said there was no one he would rather be facing than City on Wednesday.
“It was the best game we could ask for now,” he said. “The players are hurting. We had a meeting after the game and you can see all the players were really hurt by that performance and the City game is perfect. There is no hiding place on the pitch.”
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Raheem Sterling has described football’s racism problem as “deep” and “nowhere near being sorted”, and believes the organisations that run the game are not doing nearly enough to try to fix it.
The Manchester City forward has become a figurehead in the fight against racism having experienced abuse on the pitch, most recently cupping his hands to his ears in response to chants from Montenegro fans while playing for England last month.
Sterling is one of the signatories to a manifesto launched by The Times calling for more black, Asian and minority ethnic (BAME) people in positions of power, harsher punishments for racist abuse, and actions from social media companies, the media and sponsors.
Writing in the newspaper, Sterling said: “When I was a boy growing up in London, going to school and playing football, I didn’t know what racist abuse was because I never suffered any.
“So it seems crazy that, in 2019, I feel the need to write a piece in a newspaper calling for radical changes to the game that I love. But I do because the racism problem in football is so bad, runs so deep and is nowhere near being sorted.
“You will all have read about the various high-profile racist incidents in recent months: the abuse I received playing for Manchester City away to Chelsea; the booing that the black England players were subjected to in Montenegro; the nastiness that Moise Kean of Juventus endured in Italy and the endless insults thrown at players on social media.
“But that is sadly just the tip of the iceberg. Up and down the game, across the world, black and Asian players, fans and coaches are subjected to racism. Every day, from park football to the Champions League.
“In my opinion, the people who run the game are doing nowhere near enough to solve the problem. And that’s not good enough.”
Sterling would like the percentage of BAME coaches and administrators to mirror that of players in the game, while he feels punishment for racist abuse should be an automatic nine-point deduction for clubs and three games behind closed doors rather than the current starting point of a fine.
He said: “It sounds harsh, but which fan will risk racist behaviour if it might relegate their team or ruin their title bid?
“Small fines do no damage to clubs and countries, but one group of people who do have the money to make them take notice are sponsors. The next time that a club or governing body fails to act appropriately against racism, I would love to see that company pull its money out and make a moral stand.
“I don’t know how long it will take for things to change but we have to start now. I don’t want the next generation of black players to have to put up with this evil.”
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Chelsea’s Callum-Hudson Odoi is set to miss the rest of the season after rupturing his Achilles tendon in the 2-2 draw against Burnley on Monday night.
The 18-year-old was taken off four minutes before half-time after landing awkwardly while attempting to control a dropping ball and was replaced by Pedro Rodriguez.
N’Golo Kante and Gonzalo Higuain blasted two goals in as many minutes for the Blues, but poor set-piece defending allowed Jeff Hendrick and Ashley Barnes to score respond for the Clarets.
Head coach Sarri’s men did move fourth in the table courtesy of their draw, but dropping two points at home could prove costly in the Champions League race.
“Really gutted to end my season with a ruptured Achilles, gotta work hard and try and come back stronger for next season!” Hudson-Odoi tweeted.
The Englishman has played 24 times for the Blues this term and made his international debut in the 5-0 victory against Czech Republic last month.
Hudson-Odoi’s injury adds uncertainty to what will be a summer of speculation about his future at Stamford Bridge, with Bayern Munich heavily linked to signing him.