Sky Sports understands Championship duo Charlton and Sheffield Wednesday and several sides in Turkey are weighing up moves for the former France Under 21 international.
Grandin joined Palace on a free transfer last summer in a move to be reunited with former Blackpool boss Ian Holloway after impressing in the Premier League when he made 25 appearances for the Seasiders in the top flight in 2010.
The Frenchman has found first-team chances hard to come by at Selhurst Park, making just one appearance in the Capital One Cup this season, and he is considering his options during this month's transfer window.
Grandin's agent, Christian Emile, has confirmed the skilful playmaker is open to the idea of a move away from Selhurst Park as he wants to be playing on a regular basis at this stage of his career.
"Elliot has been working hard but has not got his chance to impress on the pitch for Crystal Palace," Emile told Sky Sports.
"He needs to be playing regular football so if the right club and opportunity here or abroad presents itself this January, then we will definitely consider it."