Ajax coach Frank de Boer hopes he can persuade Jan Vertonghen and Maarten Stekelenburg to commit to the club.
Belgium defender Vertonghen has been strongly linked with a move away from the Amsterdam Arena this summer, with Manchester City and Arsenal thought to be chasing his signature.
The 24-year-old, who is under contract until 2013, recently hinted he would consider leaving the Eredivisie champions, but coach De Boer is optimistic he can be persuaded to stay.
"I asked him to sign and he was positive about it," De Boer told De Telegraaf.
"Danny Blind (Ajax's technical manager) will soon hold talks with his agent.
"Jan has indicated he would move to any club, but for now he is at Ajax and seems to be happy here.
"I've given him a picture of what can happen if we stay together for another two years and then maybe he can get a better transfer."
Meanwhile, goalkeeper Stekelenburg will be out of contract next summer and is yet to pen a new deal.
De Boer is keen to resolve the future of the 28-year-old who, according to the coach, has not attracted firm interest from any other clubs this summer.
"There is currently no interest in him," he added. "We want to clarify whether he is staying or not and whether he wants to extend his current contract.
"If not, then a winter transfer seems probable."