Odemwingie unleashed a bitter Twitter rant against the Baggies during January after they rejected his transfer request.
Odemwingie, who has 15 months left on his current contract, hinted that he would look to leave the Hawthorns during the summer.
But when asked if Odemwingie could have a future with West Brom beyond the summer, Clarke said: "Yes, why not. Things happen and then life moves on.
"That's the world. It happens in life and in sport. There is a possibility, yes, and Peter is under contract for another year.
"It is not a conversation I've had with Peter. He is still trying to get back into the team."
When asked if Odemwingie's desire to leave had been expressed in the heat of the moment, Clarke said: "That's a question for Peter really. It is not one for me."
Clarke also admitted there "is a chance" Albion could turn left-back Goran Popov's loan move from Dynamo Kiev into a permanent deal.
Popov will return to the squad for Saturday's home game against Swansea after serving a three-game ban for the red card he was shown after spitting at Tottenham defender Kyle Walker.
Albion have an option to sign Popov if they desire.
Clarke said: "There's a chance (of a permanent deal). Goran has come in, has done well. He and Liam Ridgewell have had great competition for the left-back spot.
"They drive each other on for better performances and that's what I'm trying to achieve in every position if I can.
"Popov is on loan, there is an option for us to buy him in the summer, we will address that at the end of the season."