Wilson celebrates after scoring on his Manchester United debut
Wilson, who scored twice on his Red Devils debut in 2014, spent most of last season on loan to Brighton & Hove Albion and was left out of United's squad to tour the Far East.
The Daily Mail reported on Tuesday (11:48) that four Championship clubs have begun talks with the 20-year-old, though Brighton are the only ones named, along with newly-promoted Hull City.
Wilson celebrates scoring for Brighton
However, the Express & Star has credited Wolverhampton Wanderers with an interest previously.
Fulham, though, look to have won the race, with Wilson in line to become signing number 7 for Slavisa Jokanovic this summer.
The arrival of the England Under-21 striker, who's scored five times in 25 Championship outings, could pave the way for Ross McCormack's Craven Cottage exit.
Fulham could lose McCormack this summer
The Sun reported last week that Norwich City are considering a £13 million bid for the Scotland international.
Fellow attackers Floyd Ayite and Sone Aluko have already added to the Cottagers' ranks this summer, though Moussa Dembele left for Celtic at the end of his contract.
Ex-Bastia man Ayite is one of six new Fulham recruits