Current boss Craig Levein's position is under threat following a poor start to the team's World Cup qualification campaign.
Tuesday's 2-0 defeat in Belgium has left the Tartan Army bottom of Group A with just two points from their first four games.
When asked if he would consider the role, Clarke told reporters: "No, no. I'm under contract here at West Bromwich Albion."
Clarke won six caps for Scotland during a brief international career.