Reports in England suggested that West Ham and Newcastle were interested in the player.
The 29-year-old moved from Chelsea two years ago for about �8m, but injuries and competition for places in attack have limited his chances in the first team.
Last season, Gudjohnsen was moved to a midfield role by coach Frank Rijkaard, although he rarely completed 90 minutes in a match.
The Icelandic player, along with a host of other players, is believed to be surplus to new coach Pep Guardiola's plans for next season.
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