The Red Devils are seeking to improve their striking options in the January transfer window.
ESPN claims Wilson is among the Old Trafford club's top targets for a mid-season move.
Moussa Dembele from Lyon is another attacking target, while the club also wants to sign winger Jadon Sancho.
Wilson is 27 and has a long-term contract with the Cherries.
They would not want to lose him for cheap, given his importance to the team.
Wilson has five goals in 14 games this term.