Stekelenburg has been linked with a host of clubs around Europe, including Manchester United, Arsenal and AC Milan.
Schalke are looking to bring in a replacement for Manuel Neuer, who is expected to leave the club this summer.
“Stekelenburg is the shot-stopper of Netherlands’ national team for a good reason, and his contract with Ajax runs [for] only one more season,” stated Schalke sporting director Horst Heldt to WAZ.