Manager Mark Hughes has revealed the Bosnia international is doubtful for the KC Stadium clash after suffering the injury in training.
Thomas Sorensen, who has not started a league game since the final day of the 2011-12 season, is on standby to replace him.
Hughes told the club's website, www.stokecityfc.com: "Asmir is the big worry for us at the moment, because of a knock he has picked up to his thigh on Tuesday.
"He has a bit of bleeding in there, so we need to nurse him and then assess him tomorrow to see where he is at.
"It is a bit of a concern because he has been outstanding for us this year, but we will see what happens over the course of the next 24 hours."
Sorensen, 37, has been restricted to domestic cup ties in the past two seasons but Hughes has no doubts over the Dane's readiness to play.
He said: "If Asmir isn't ready then I will have no qualms in throwing Thomas into the team.
"He is a top keeper in his own right who has an abundance of experience behind him."
The Hull game will come too soon for midfielder Matthew Etherington despite his return to training this week after a back injury.
Hughes said: "Matty has joined the squad again in training this week but I think it will be more worthwhile letting him recuperate back here this weekend, rather than sitting in a coach for three hours.
"We will hopefully get him involved in the under-21 game for a spell tomorrow afternoon, which will help him build up his match fitness again."
Full-back Erik Pieters is fit again after a groin strain but Hughes may opt to retain Marc Muniesa, who impressed in the Dutchman's absence in last week's shock win over Chelsea.
Hughes said: "It's a very nice problem to have two quality players battling for one position.
"Erik has been fantastic this season, but Marc was outstanding against Chelsea. It's one that I will have to sleep on."