De Telegraaf says the Dutch giants wants to offer the youngster a new deal sooner rather than later.
Eriksen made his debut for Ajax in the 1-1 draw with NAC earlier this season.
“Christian recently turned 18 and we can now offer him a lengthy contract. His current contract is due to expire in the summer of 2011,” said head coach Martin Jol.
“However, we are eager to offer him a new contract in the upcoming weeks. We want Christian to stay in Amsterdam for several more years. It all depends on what the player himself wants though.”