The 32-year-old has had a miserable time at Fenerbahce since moving from Old Trafford and the Blues could be set to offer him an escape route.
The Daily Express claim any raid for Van Persie depends on whether the Premier League champions are able to complete their loan deal for Brazilian striker Alexandre Pato.
With Radamel Falcao injured and Loic Remy being chased by the likes of Newcastle and Crystal Palace, Guus Hiddink is looking for a backup striker to support Diego Costa.