Olsson signed a new four-year deal with the Baggies two months ago but reports in his native Sweden claim there is a £3million get-out clause.
The centre-back has been linked with potential moves to Arsenal and Fenerbahce.
But Clarke has made it clear none of his major players will be moving from Albion this month.
Clarke said: "I don't do contracts, it's not my job. The ins and outs of Jonas' contract are personal.
"I don't think it's right for me to sit and discuss it with you at this moment in time. But why would I expect to lose him?
"We can hang onto every single player. We don't have to sell anybody.
"It's not unsettling for me because I know that come February 1, the players that I need to be here will still be here.
"Why would I expect to lose him in January? I told you, it's complete speculation about Jonas Olsson.
"It's a silly season. January is a silly season."
Clarke is willing to allow unsettled midfielder Graham Dorrans to leave the club this month if the price and circumstances are right.
But he believes he already has a ready-made replacement in George Thorne, who has returned from a successful loan spell at Peterborough and was chosen against Manchester United last weekend.
Clarke said: "Graham will go if there is a suitable offer for him and it suits the club and it suits Graham.
"I've got a replacement, I've got George Thorne back. His loan spell has helped him a lot and he did very well at Old Trafford.
"Even when he came into the game (against Fulham) the other day, he showed that he has improved. We got some great reports from Peterborough. It was just what the boy needed.
"He needed regular football. We're grateful to Peterborough for giving him the chance to have that. I've always known he has big potential."