The Amsterdam-based outfit are keen for the 20-year-old to sign an extension to his deal, which is due to expire in the summer of 2014.
However, amid speculation of reported interest from Premier League side Liverpool, the Danish international has opted against signing fresh terms for the time being.
"Christian has informed us that he doesn't want to sign a new contract right now," Ajax's technical director Marc Overmars told Sporten.dk. "I think he and his agent want to see what opportunities present themselves this summer.
"We want him to stay here for at least two more years, but the day he leaves us, he will be ready to play for the very best. He's a player even the biggest clubs in the world could do with having in their squad."
As well as Liverpool, the likes of Manchester United and Manchester City have previously been linked with the midfielder.