The 32-year-old is poised to depart the Potters just six months after arriving at the Britannia Stadium having failed to make an impact at the Premier League club.
Gudjohnsen, who has made just five appearances for Stoke, is out of contract in the summer and can leave on a free transfer.
The Iceland international says he will turn down big-money offers from the United States and Dubai in favour of a move to Amsterdam, even if it means accepting a cut in wages.
"I'm able to sign large contracts in America and Dubai, but my preference is to go to Amsterdam," Gudjohnsen told the Daily Star.
"It is not about money. The sporting challenge is paramount because my career would gain a new impetus.
He 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."
Gudjohnsen, who joined Stoke from Monaco last year, has spent time at Chelsea, Tottenham and Bolton.
The veteran hitman, who began his career at native club Valur Reykjavik, has won 63 caps for Iceland.
