The news comes after the Belgium international supposedly had a bust-up with fellow midfielder Morgan Schniderlin in training ahead of their home fixture against Watford in which the pair were both dropped for.
When Moyes was the Everton manager he signed the 30-year-old from Olympiakos but the winger has struggled to make any kind of impact at the club lately. He has scored just 29 times in 150 appearances in his five-year stay at the club.
Moyes is prepared to take a chance on one of his former players as the Belgian has fallen out with current caretaker boss David Unsworth.
The attacker did sign a new three-year extension at the club just six months ago but it looks as though there is no future for him at Goodison Park and Moyes could take the gamble when the window opens in January.