The midfielder had a recent trial spell with The Toffees, after Rennes revealed he could seek out a new home.
Delaye reportedly impressed Toffees chief David Moyes, but not sufficiently to win a deal.
He returned to France having failed to win a deal with Everton, but he could be on the move again - with Corsican outfit Bastia said to be considering lodging a bid.
Delaye's situation should be clarified over the course of the weekend, with the transfer window set to slam shut on Monday.