Swedish international Olsson is in the final year of his contract and has attracted interest from Tottenham.
Odemwingie, the Baggies top scorer last season, has also been the subject of speculation over his future.
Clarke said: "I said a few weeks ago that I expected to keep both of those players - and nothing has changed.
"I did expect to keep them and it looks as though they are going to stay.
"There is no dialogue or conversation that I've had with Dan Ashworth (technical and sporting director) that makes me think there has been anything (offers) for the players."