The former Chelsea striker could be on the move again this Summer after Besiktas failed to secure UEFA Champions League football.
The report goes onto state that Ba could team up with his former manager Alan Pardew at Crystal Palace. The Senegal international played under Pardew while at Newcastle United.
The Senegalese international has scored a total of 28 goals and provided seven assists in all competitions this season.
Ba also broke a personal best scoring 18 league goals for the first time in a single season in his career.
Beşiktaş finished the league season in third place and will play in the Europa League next season.
Crystal Palace finished the season in 10th place with 48 points in 38 games.