He started 32 of his 33 appearances last term but he has been less of a first-team regular under Sam Allardyce, making the starting XI on 19 occasions and scoring just twice.
And his lesser role has led Allardyce to believe the 31-year-old now has his eyes set on a move to Ligue 1 outfit Marseille.
Speaking ahead of a trip to face Premier League leaders Chelsea at Stamford Bridge on Saturday, Allardyce says any potential switch would first depend on Marseille making a significant offer.
"[Cabaye] would like to keep the club up," the Palace manager told a pre-match news conference. "Reading between the lines, he would like to go to Marseille if they made a big enough bid for him.
SA: All of us have to get better in the final third. We're not as creative or as clinical as we should be at the moment.— Crystal Palace F.C. (@CPFC) March 31, 2017
"In today's world and today's society, if he does the job for us and keeps us up and Marseille offer us millions of pounds, then Steve [Parish, chairman] will say 'Should we or shouldn't we'.
"But I would prefer to keep him.
"What happens [at the end of the season]? Who knows? There will be some comings, there will be some goings and that happens at every football club now. Too much these days."