Chairman Adam Pearson said: "The two players have turned down the new deals. We could not agree terms and so we've decided to withdraw the offer. We have no plans at this stage for any further discussions."
He added: "Under the terms of their current contracts Ian and Theo are now free to talk to other clubs but should they leave before the end of the season we would be asking for a fee."
A year ago Theo Whitmore was involved in a car crash, seeing team-mate Steve Malcolm die. Earlier this season Ian Goodison had a motorbike crash leaving the cultured defender on the sidelines for a spell.
Numerous Division 1 clubs have shown interest in them in the past, and may take up the opportunity to sign the international stars on Bosman free transfers.
Recent signings of Richard Sneekes and Matthew Wicks leave the Tigers covered if Goodison and Whitmore go.