The 28-year-old Portuguese international has been a star for the London club since joining them and he managed to make an immediate impact in the Premier League last season.
As a result, Liverpool were eyeing up a summer move for the player.
However, the midfielder has now picked up a shoulder injury and his asking price has proven to be prohibitive as well.
Football Insider claims that Liverpool have now cooled their interest in the player.
The Reds to add some defensive steel to their midfield and it remains to be seen whether they can bring in the right reinforcements before the window closes.
They were linked with players like Romeo Lavia and Moises Caicedo recently but both players have now joined Chelsea instead.
Palhinha could prove to be a quality addition to the Liverpool midfield alongside Dominik Szoboszlai and Alexis Mac Allister. However, Fulham will have to lower their demands in order for the move to go through.
The Portuguese star is reportedly valued at £90 million and his suitors are unlikely to pay that kind of money for him.
Liverpool have looked vulnerable defensively against Chelsea and Bournemouth so far and they must look to sign a reliable defensive midfielder before the window closes.
The likes of Fabinho and Jordan Henderson have moved to Saudi Arabia and they will need to be replaced.
