The Wales midfielder is enjoying career best form this season - just as his current deal runs down.
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BBC Sport says negotiations over a new agreement have now hit a road-block.
Aston Villa, Brentford, Everton and Crystal Palace are all interested in Wilson, though Fulham are insisting he won't be sold this month.
Indeed, Wilson is open to staying with the Cottagers, but is seeking clarity on manager Marco Silva's future, with the Portuguese's contract also expiring in June.
