The Nigerian striker has had a turbulent campaign following the January transfer window when he failed to orchestrate a move to Queens Park Rangers without the club's permission.
"His situation is something we will have to consider at the end of the season," Goal.com quotes Clarke as saying.
"It's a decision for us all to sit down at the end of the season and make. We need to decide what is the best way forward for the football club."
Since Odemwingie's failed transfer, the 31-year-old was fined two weeks' wages for criticising the club on social network website Twitter.