The Iceland international has failed to settle in Ligue 1 and the likes of Blackburn, West Ham and Tottenham are all thought to be keen on bringing Gudjohnsen back to England.
His father and agent Arnor Gudjohnsen admits the 31-year-old is thinking about making a return to England in this month's transfer window.
"I am not sure what he is going to do," Gudjohnsen Snr told the Daily Mirror. "He is going to take the next two weeks to decide. He could stay. He is very open. Nobody knows yet.
"He is obviously seriously thinking about a return to England but he has not made any decision. It is in his hands."