Clarke confirmed Odemwingie is part of his plans to face Sunderland, returning to favour after his Twitter rants against the club and the bitter on-off transfer saga with QPR last month.
Head coach Clarke knows some supporters will be in no mood to forgive Odemwingie but he has asked them to put any negativity towards the Nigeria international to one side.
Clarke said: "I understand some of the supporters might not want to forgive Peter quickly but, when they go to the stadium, all I ask is they support the team.
"If Peter scores a hat-trick and they choose not to celebrate Peter's goals, they should celebrate the fact that the team have scored.
"All we can ask is that the supporters support the team and don't allow their feelings over one player to over-ride the fact that the support has been great this year, home and away."
Clarke admitted Albion's shortage of options means Odemwingie will play again this season.
He said: "We've had a couple of little chats but nothing in-depth and he knows the situation.
"He knows he needs to work hard and he has to be ready for his opportunity when it comes and, for sure, it will come, because we only carry a small squad.
"Will he be considered for Saturday? Absolutely. I've got 20 players available and he'll be involved with the 20 players."