Wilson has emerged as one of the Premier League’s in-form players.
He has scored six goals in his previous 12 games in all competitions – taking his season’s tally for Fulham and Wales to 12, with five direct assists.
It is understood a number of top-flight clubs have expressed an interest in signing Wilson during the window, with Aston Villa, Brentford, Everton and Crystal Palace among those monitoring his situation before the 2 February deadline.
Several English and European sides are expected to join the race in the summer if he leaves on a free transfer.
Fulham have held talks with Manchester City over a potential £35m deal for Oscar Bobb, who also operates on the right side of attack.
If the Cottagers can pull off a deal for Bobb, 22, it remains to be seen as to whether the club’s stance on Wilson changes later in the transfer window.
Wilson joined Fulham from Liverpool in 2021 – initially on loan – in a deal worth £12m and has made 171 appearances, scoring 33 goals.