Tottenham have shown an interest in bringing in Gudjohnsen on loan for the rest of the season, but Spurs boss Harry Redknapp believes West Ham have beaten them to the former Barcelona and Chelsea forward's signature.
Redknapp expects Gudjohnsen to join West Ham but confirmed they had made an inquiry about taking him on loan for the rest of the season, with his parent club Monaco paying the bulk of the wages.
"I spoke to his agent, he said he was going to West Ham, so I left it with the agent," Redknapp said after the Barclays Premier League win over Fulham.
"I would take him on a loan. He would be good loan signing playing in different systems.
"He's a good footballer and an interesting player on a loan but I think he's gone to West Ham."
Gudjohnsen was believed to have undergone a medical at Upton Park on Tuesday evening with a deal likely to be sealed in the next 24 hours.