Arnor Gudjohnsen, who acts as his son's agent, referred to Hammers chairman Eggert Magnusson, a compatriot of the family.
"I have heard about the interest from West Ham, but there have been no talks as yet," he told Sky Sports.
"It would be something Eidur would consider as there are some Icelanders there, with the owners and all.
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"If they are interested in Eidur I am sure they will contact me."
Gudjohnsen's place at the Camp Nou is under threat following the close season acquisition of Thierry Henry, with superstars Ronaldinho, Lionel Messi and Samuel Eto'o already in place.
The 28-year-old, who only joined from Chelsea a year ago, is working his way back from injury.
"He is currently injured and he is focused on getting fit again, but he will consider all options open to him," Gudjohnsen Sr. continued.
"Barcelona have always told him it is up to him what he wants to do and they will not stand in his way if he wants to go and they will be happy for him if he wants to stay.
"Eidur will not rush a decision on his future and we will evaluate every option we have."
Barca lost out to Real Madrid in the race for the Liga title on the final day of last season, while the Hammers have cash to spend after biscuit magnate Magnusson's takeover at Upton Park.
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