The Daily Star says Gudjohnsen is willing to take a huge pay-cut to end his Stoke misery - with a move to Dutch legends Ajax.
The Icelandic striker, 32, can leave the Potters for free just six months after signing up.
"I'm able to sign large contracts in America and Dubai, but my preference is to go to Amsterdam," said Gudjohnsen, who has made just five appearances since moving from Monaco.
"It is not about money. The sporting challenge is paramount because my career would gain a new impetus."
The former Chelsea hitman added: "Because my contract is up at the end of the season, I can already leave Stoke for free.
"I even think that if Ajax can do a deal, Stoke will pay a portion of my salary. I'm willing to settle for much less."