The Dane's agent claimed back in October that his client had rejected the advances of the Premier League champions as he was keen to continue developing in the Netherlands.
However, Eriksen has now revealed that he may not be prepared to sign a new deal with his current club, opening the door for City to make a second advance.
"I feel good at Ajax and the club want to make a new deal," he told Sporten.dk.
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The Denmark international's contract runs until the summer of 2014 but the club's technical director, Marc Overmars, has revealed that the Amsterdam ArenA outfit want to discuss a new deal at the start of next year.
"We would like Christian to sign a new contract, but he still does not know what he wants," he explained.
"Conversations with him and his agent have taken place and we will see what happens after December."
Former Barcelona winger Overmars also stated that the club have had no contact with other sides regarding the sale of their prodigious talent but has vowed to help the youngster make the correct decision for his career.
"At this moment, we have not heard from other clubs," he continued. "It is Christian's choice in any case and it is important that he makes the right choice. Together with Ajax we will make sure he is fine."