The 28-year-old Netherlands international had surgery on a fractured thumb he suffered in training last week and will now be sidelined for around two months.
Arsene Wenger and Sir Alex Ferguson, among others, are thought to be monitoring Stekelenburg, who impressed as part of the Dutch team that lost 1-0 to Spain in the World Cup Final last summer.
And the stopper has revealed that should an offer to join the likes of the Gunners or Red Devils come up, he would be open to a transfer away from the Eredivisie.
"You never know. I have possibly played my last game for Ajax. I still have one year left on my contract. If something appealing comes up then I will certainly consider it," he told NOS.
Emirates Stadium supremo Wenger recently turned to veteran German stopper Jens Lehmann to help ease the Gunners' goalkeeping crisis following injuries to Wojciech Szczęsny and Łukasz Fabiański.
Ferguson, meanwhile, continues to be linked with goalkeepers as he seeks a long-term successor to Edwin van der Sar, who is hanging up his gloves at the end of the season.
Jeroen Verhoeyen has taken over in goal at the Amsterdam Arena following Stekelenburg's injury, and the latter was full of praise for his deputy, regardless of criticism in the media.
"[He is] an outstanding goalkeeper. I don't understand everything what is being said in the media about him," he said.
By Jake Svensson
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
