Allardyce said, "I would have thought he would like to stay on, being as we've looked after him so well."
"There's no better place these days for Ivan to play his football than with us."
Meanwhile, Bolton Wanderers are being linked with Racing Genk whizkid Steven Defour.
The 18 year-old midfielder has told Genk officials he plans to leave at the end of this season and was watched in action against Lierse last month by Bolton, Sampdoria and Ajax.
Genk president Jos Vaessen has revealed Ajax have already made an approach: "They sent us a letter to ask us for a transfer fee and now they think that they are allowed to speak with player too.
"That is not the case but we can do little about it."
Bolton are also reportedly chasing Middlesbrough midfielder George Boateng.
The Holland international's contract is expiring and the player has yet to agree terms on a new deal which has alerted Sam Allardyce.