The Crystal Palace winger is a hot property and will be on the market in the offseason.
Per ESPN, new co-owner Sir Jim Ratcliffe wants to bring Olise to Manchester in the summer.
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The Frenchman has scored seven goals and added four assists in only 16 games this season.
While injuries have disrupted his campaign, United do not believe they are long term problems.
Olise does have a release clause, but will be wanted by a host of top Premier League clubs.