Van Persie's fellow Dutchman, Frank de Boer, has been appointed as Crystal Palace's new manager.
Van Persie, who scored 144 goals in 280 Premier League appearances for Arsenal and Manchester United, is currently on the books of Turkish giants Fenerbahce.
Robin Van Persie upon signing for Manchester United
However, the 33-year-old is about to enter the final 12 months of his contract at the Ülker Stadium, and could be on the move this summer.
According to Skybet, a return to Feyenoord, the club at which Van Persie began his career, is the most likely scenario at 7/4, although Crystal Palace are second favourites at 8/1.
The Eagles, who are believed to be in the market for a striker this summer, appointed Van Persie's fellow Dutchman, Frank de Boer, as manager on Monday afternoon.
And while the pair's careers are yet to intertwine, they could put a stop to that at Selhurst Park this summer.
New Crystal Palace boss Frank De Boer
Van Persie has played against Crystal Palace five times in his career - winning all but one of those encounters and scoring two goals.
Could Crystal Palace bring Van Persie back to London?