Ole Gunnar Solskjaer thinks the in-form Manchester clubs could serve up a thrilling derby encounter on Sunday.
United are unbeaten in nine games, following Thursday's 3-0 FA Cup win at Derby, and will now look to boost their Champions League qualification prospects when City visit Old Trafford on Sunday.
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- Solskjaer hails Ighalo's Man Utd impact
- Maguire doubtful for Manchester derby
Solskjaer said: "They will feel confident. They have hit form, they are playing well. They have just been to the Bernabeu, winning there as well, and won the cup final.
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"So I am sure they will play their game, we will play our game, and hopefully it will be a good one. Let's hope it will be a 4-3, like we have seen before. There have been many classics. We will do what we can to make it a classic."
There have more derbies than usual this season, with United and City playing a two-legged Carabao Cup semi-final in January.
City won that 3-2 on aggregate, while United won the season's first Premier League meeting 2-1 at the Etihad in December.
"There is not going to be any video Friday or Saturday, because we played them enough times," Solskjaer added. "I think it helps because our team is developing and you want to play against the best.
"We want to learn and they have been the best for the past few seasons. For us, it's a great challenge."
The race for a top-four place has tightened up in recent weeks and United are three points behind Chelsea in fourth, with Wolves, Tottenham and Sheffield United also in the mix.
"We have just got to concentrate on ourselves and keep improving and keep getting results," said Solskjaer. "But I know it's going to be tight.
"Wolves are definitely putting up a challenge as well. There are loads of teams that want to get in the top four and we are one of them. We just need to manage our squad well enough, rotate well enough, and these next few games, they are important.
"If we can get six points from Manchester City and Tottenham [March 15], then we are giving ourselves a good chance."
Ole Gunnar Solskjaer sang Odion Ighalo's praises after the Manchester United striker scored twice in the 3-0 FA Cup fifth-round victory over Derby County.
Ighalo arrived at Old Trafford to much derision in the January transfer window, having spent the past three years playing in the Chinese Super League after a similar length spell at Watford.
But in just two starts for United, against Club Brugge in the Europa League and Derby, boyhood fan Ighalo has netted three goals.
"He is doing what it says on the tin and what we asked for when we signed him," Solskjaer said.
He is coming in, playing up front, and he's a different type of striker. He scores, he gets chances every game and today he could have had another couple. I am very happy with him. It gives us a chance with Mason (Greenwood) and Anthony (Martial) to keep them fresh as well."
Harry Maguire is doubtful for Sunday's Manchester derby after missing Manchester United's FA Cup tie at Derby with a slight ankle injury.
The England international faces a race to be fit to face neighbours Manchester City, in a vital match for their top-four hopes.
"It is touch and go because he rolled his ankle and twisted his ankle," manager Solskjaer said on Thursday. "But hopefully he will recover quickly. I wasn't going to rest him today. I didn't give him the day off birthday wise. So I hope he will be fit."
Maguire expressed his disappointment on social media after he was ruled out of the match at Pride Park on his 27th birthday.
He said: "Disappointed to miss out through injury - Working hard to get fit ASAP. Good luck to the lads."
Sky Sports News' North West reporter James Cooper:
'When Solskjaer came to Manchester in 1996, United and City were in different divisions, but injuries also limited his involvement. Tellingly, his record for United against City as a player reads; four matches played, zero wins.
'He was part of two victorious squads as an unused substitute and such lessons have taught him a great deal about how to tend to his own flock, about his players' determination and the ability of some to soar when a big opportunity is offered.
'Right now the United manager is in a good place. He has masterminded a nine-game unbeaten run consisting of six wins and three draws in all competitions with just two goals conceded, the latest success coming on Thursday night with a comfortable 3-0 win at Derby to set up an FA Cup quarter-final clash at Norwich.
'Watching his players go through their paces too at Carrington, it is easy to see the benefits of finding some momentum. There is plenty of laughter and Solskjaer feels his squad are starting to believe they really can defeat the sides they are confronted with, a belief he and his team-mates had in abundance when they were wearing the famous red shirts.'