The 22-year-old nearly joined Chelsea in the summer after they triggered his £35m release clause but opted to sign a new deal at Selhurst Park instead.
The Palace attacker signed a four-year contract with The Eagles, and it is understood that terms regarding a new release clause were also inserted into the updated contract.
While the exact amount of the new release clause is still unknown, it is believed to be significantly higher than the £35m clause in his old deal.
The new release clause is expected to become active in the summer, and football.london reports that Man United are keeping tabs on Olise, who is currently sidelined due to injury.
The report adds that Olise is widely expected to leave Selhurst Park at the end of this season, and while Chelsea maintain an interest in acquiring his services, the winger would prefer a move to Old Trafford instead.
While Liverpool and Arsenal had been previously associated with potential moves for the Palace winger, it seems that Chelsea and Man United are currently the front-runners in the transfer battle.
Olise was a part of the Chelsea academy from the age of seven to 14 but is a lifelong supporter of The Red Devils.
United are expected to be in the market for a new winger in the summer, with Jadon Sancho set to leave the club permanently after his public fallout with Ten Hag last year.
Antony is another that could be on the chopping block, having failed to hit the heights expected during his time in Manchester.
United have faced difficulties in attack this season, with midfielder Scott McTominay currently leading the goalscorer standings with five goals to date.
Despite limited playing time this term, Olise has managed to score five goals in just nine league games and is the team's second-highest scorer behind Odsonne Edouard on six.
The France Under-21 arrived at Selhurst Park back in the summer of 2021 on a five-year deal for a fee of around £8.3m from Reading.
The winger has made 72 Premier League appearances for The Eagles since his arrival, scoring nine goals and providing 17 assists during his time in London.