The Red Devils want to add firepower to their front line after a season of struggles in front of goal.
Per Fabrizio Romano, they have identified the French winger as the ideal target.
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Whether Olise wants to move to United is unclear, as he may have his pick of clubs.
The winger will have a release clause activated in his contract, which means every top Premier League club may bid for him.
United will have to work hard to get a deal over the line, but may be able to do so by promising Olise regular game time.