The Icelandic striker has not enjoyed a particularly positive time at the Britannia Stadium and is believed to be prepared to take a pay cut to exit the club.
"I'm able to sign large contracts in America and Dubai, but my preference is to go to Amsterdam," said Gudjohnsen.
"It is not about money. The sporting challenge is paramount because my career would gain a new impetus.
"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."