Swedish international defender Olsson, who is in the final year of his contract, was linked strongly with a move to Tottenham earlier in the summer.
Striker Odemwingie, the Baggies top scorer last season, has also been the subject of speculation over his future.
But Clarke is now optimistic the duo will stay, with no last-gasp attempts expected to prise Olsson and Odemwingie away.
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."
Olsson has been the lynchpin of the Baggies back four during successive seasons in the Barclays Premier League.
Nigerian international Odemwingie followed up his 15 goals in his first season by again reaching double figures again during the 2011-2012 campaign.
Clarke is looking to bring in a left-back with Martin Olsson (Blackburn) and Bryan Oviedo (Copenhagen) on his radar, but he is not expecting any major transfer business before the window shuts.
He said: "I'm not particularly hopeful. There are about 30 hours left in the window and, as I sit here now, it is probably more likely we won't do much business or any business.
"Put it this way, there will be other clubs that are busier than we are going to be.
"There have been lots of rumours and lots of names bandied around. It is not correct for me to sit here and speak about players at other clubs.
"We go about our business quietly, we've got targets. I've said for a couple of weeks now if the window was closed, I'd be happy with the squad I've got.
"I sound like a broken down record but I would be. Honestly, the quicker the window closes, the better."
