The former Barcelona and Chelsea striker is wanted by Swansea manager Brendan Rodgers, who knows the player from his time at Stamford Bridge.
Gudjohnsen, 32, has failed to score for Stoke in only five appearances and boss Tony Pulis has been disappointed by his overall fitness levels.
On his way out: Eidur Gudjohnsen has failed to impress at Stoke City
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Explore more:People: Eidur Gudjohnsen, Tony Pulis, Brendan Rodgers Places: Barcelona