The 32-year old Iceland international joined the Potters from French club Monaco in August on a one-year deal but has only been deployed in four substitute appearances in the league, with his last piece of action coming in the Carling Cup loss to West Ham United in last October.
Potters boss Tony Pulis is well aware of Gudjohnsen's situation but is keen to keep him at Britannia Stadium for future reference.
"He needs the opportunity as much as anything else," Pulis said.
"Someone asked me the other day 'are you going to play Eidur?' But who are you going to leave out?
"We'll need the squad because we'll start picking up injuries and suspensions."