The Sun reports that City have now entered the race to sign the Crystal Palace winger, who is one of the hottest young properties in England.
Pep Guardiola is said to be a big fan of the France Under-21 international and believes he can be a long-term solution on the right wing.
The news will come as a big blow to United and Arsenal, who have made Olise one of their top targets this summer.
United need a new right winger as their current options have all failed in the role. Antony has scored only one goal this season, while Jadon Sancho has been loaned to Borussia Dortmund and Mason Greenwood exiled to Getafe.
Arsenal are looking for an alternative to Bukayo Saka.
Olise, 22, has emerged Premier League’s most promising young players and he is being chased by many other big clubs in England.
The France U21 international has six goals and three assists in just 11 league games so far this season, and he has shone despite several injury issues.
However, Olise’s time at Selhurst Park is coming to an end, with it widely reported that he will be allowed to leave Crystal Palace during the upcoming summer transfer window.
He signed a new four-year deal at the south London club back in August after rejecting a move to Chelsea, but Olise will likely leave Palace as they look to rebuild the squad using his transfer fee.
Premier League giants want Michael Olise
Manchester United have internally discussed the possibility of signing Olise this summer and the suggestion of using Aaron Wan-Bissaka as a makeweight in the deal has been talked about.
However, some members of staff have expressed their concern over pursuing Olise due to the fact both Wan-Bissaka and Wilfried Zaha struggled with the step up from Crystal Palace to Old Trafford.
Chelsea also have a long-standing interest in the player, while Liverpool are also keen as they look to sign an eventual heir to Mohamed Salah.
But now City have also entered the race.
FootballTransfers understands that Olise currently prefers a move to Arsenal due to the fact he grew up as a Gunners fan. He would naturally compete with Bukayo Saka for a starting spot at the Emirates Stadium, but we have been told that Mikel Arteta is considering moulding Olise into a right-sided number eight.