It is understood that Everton made a move for the 28-year-old last week but Fulham turned it down.
The Wales international is out of contract this summer and could leave for free. Fulham are determined not to sell him this month.
Head coach Marco Silva has also said there is no chance of Wilson being sold in the January transfer window.
Instead the club is focused on securing his future. They signed him on an initial loan from Liverpool in July 2021. Since then he has played 173 games for Fulham scoring 34 goals and providing 43 assists.
However, talks over a contract extension are currently on hold because of transfer interest as BBC Sport revealed in January.
It is also understood that Wilson would like to know what will happen with Silva who is also out of contract this summer before deciding on a new deal.