Dorrans has struggled to secure a first-team spot and was left out of the Baggies matchday squad altogether for the New Year's Day home defeat to Fulham.
The 25-year-old held talks with Clarke two weeks ago and is understood to be keen on a move nearer to his native Scotland.
But Dorrans will only go if Albion receive an offer which matches their valuation and if they have sufficient numbers in the midfield department.
Youssouf Mulumbu will be on African Nations Cup duty with DR Congo while Claudio Yacob is currently sidelined with a hamstring injury.
Clarke said: "Graham came to see me a couple of weeks ago and he said it (wanting to leave) was down not to because of what is happening this season but previous seasons.
"He feels as though he needs a fresh challenge. We had an amicable discussion.
"We came to an agreement that, if something came along in January that was good for the club and good for Graham, we would listen to the possibility that Graham could leave."
Clarke also dismissed reports linking defender Jonas Olsson with a move to Arsenal as "speculation."
Olsson is reported to have a get-out clause in the new four-year contract he signed earlier this season if certain clubs make an offer.