Gudjohnsen joined the Potters from AS Monaco on a one-year deal in August but has made just four Premier League appearances all off the bench since his arrival at the Britannia Stadium.
Now Pulis is ready to get rid of the former Chelsea man if the right bid comes in for him.
"If there's deal you think is right for the club and the player thinks is right for him, then you get the deal done," he said.
"If it's not, then you don't. Eidur has been unfortunate in that he hasn't had the game time he would've wanted.
"And with the bad weather of the past three weeks, he hasn't been able to play in the reserves.
"But he's come in on his days off and worked hard - he's just been unfortunate."