The French striker has benefited from the chance he has been given at Goodison Park but with his deal set to run out at the end of the season he is free to move away for nothing.
Reports in the French media say that Roma, Bordeaux and Atletico Madrid are all tracking Saha, but boss David Moyes is still hoping he can be persuaded to sign a new deal at the club.
He said: "His contract is up at the end of the season, so he could speak to foreign clubs in January.
"We have been speaking to him. We're happy with him and we'd like to keep him here."