Fulham value Joao Palhinha at double the £30m bid they have rejected from Bayern Munich.
Barcelona and Manchester United are also interested, but it is unlikely the Spanish side would be able to afford him and there is uncertainty surrounding the managerial situation at Old Trafford.
There is no release clause in the new Fulham contract Palhinha signed last September. The deal runs to 2028 and Fulham have the option to extend it by another year.
Fulham retain an interest in Fluminense midfielder Andre amid uncertainty over Palhinha's future. Andre is one of a number of midfielders the club are looking at should they ultimately need to replace him.
Palhinha almost moved to Bayern on Deadline Day last summer. Fulham also turned down a £45m bid from West Ham last July.
New Bayern boss Vincent Kompany is eager to bring the Portugal international to the Bundesliga with backing from sporting directors Max Eberl and Christoph Freund.
Bayern are understood to be willing to pay up to £38m for the 28-year-old.