Bayern Munich are currently favourites to sign the midfielder after failing to do so in the summer.
The German champions were ready to splash £60million on Palhinha, but a deal collapsed on deadline day as Fulham could not sign a replacement.
Fulham are now working on a deal for Fluminense midfielder Andre, who has also been scouted by Liverpool and Manchester United, with CEO Alistair Mackintosh flying out to Brazil last month for talks.
Palhinha in September signed a new contract with Fulham until 2028, however, Bayern remain undeterred ahead of the January transfer window.
They will face competition for his signature, though, as Standard Sport understands multiple Premier League sides are also tracking the 28-year-old.
Palhinha cast doubt over his situation last month when he said: “I don’t know what will happen in the future.
"Nobody has given me anything in my career, everything I’ve achieved is down to my worth, my work.
“I’m 28, but I know I can go higher and I’m looking to the future with that ambition.”
Bayern are in the market for a holding midfielder and defenders this winter, with sporting director Christoph Freund confirming they are still pursuing Palhinha.
“Of course he is still on our radar,” he told Bild. “The club worked intensively with Palhinha in the summer.
“I was there for a bit on the last, strange day of the transfer window. But you can’t say yet what will happen. We are generally exploring the market.”
Palhinha has excelled in the Premier League since joining Fulham last year from Sporting Lisbon for around £17m.
He made 47 more tackles than anyone else in the League last season and is leading the way again this term.
“To be honest I always looked to the Premier for the best league for me as a player,” Palhinha told Fulham Fix Podcast last week.
“My characteristics, what I want to do on the pitch, for me it is the best league that I fit… for me it is the best league in the world.”
Palhinha was disappointed a move to Bayern broke down in the summer, but he has since knuckled down and performed well.
“I am feeling content because I am playing, I am doing my job, I am focused here,” he said. “It is something that nobody can point the finger to me and say ‘you don’t respect’. I always did my work here, I respect everyone — the staff, my team-mates and my history at the club. I don’t want to screw up what I have built here.
“But I can’t lie. Of course it is the opportunity of my life that happened. If something like Bayern happens in your life, you can’t think of anything else. In football we are always fighting to achieve good things.
“I grew up dreaming of this kind of opportunity. I don’t know if it is going to happen again or not. I just want to make my job like I have been doing, keep improving because I know I have much more to improve.”