The Romanian international full back has been linked with a number of clubs since having an impressive Euro 2000, but entered negotiations to extend his deal, which still has five years left, last month.
Juventus and Milan duo AC and Internazionale have already considered attempting to secure the highly-rated 19-year-old's future, although firmer interest came from Barcelona and Galatasaray.
However, Fiorentina coach Fatih Terim has admitted his interest in the player, and could now be set to make a move during the Italian transfer window this month.
It is, though, more likely that Chivu will stay at the Amsterdam ArenA until 2002 at the earliest, and then look to move to one of Europe's top clubs.
Meanwhile, Ajax have completed the signing of highly-rated South African midfielder Steven Pienaar, who has signed a five-year contract with the club.
The 17-year-old, who has been tracked for some time and agreed a switch from Ajax Cape Town in the summer, spent two weeks finalising the deal and completing a medical.
The former South African Young Player of the Year is now likely to play in the Ajax second team before being introduced to Eredivisie action.
