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However, Tigers Chairman Adam Pearson says that if they show their worth then the club may be prepared to re-enter contract negotiations.
"The situation with Ian and Theo is that we would be prepared to look again at the end of the season - if they prove they deserve new contracts.
"This isn't a climbdown. If someone came in to sign them then we would consider any approach. However, we're not slamming the door shut on them. It's more a case of keeping all our options open. Ian and Theo know that they have to do if they want to stay at this club. The ball is in their court."
Whitmore last started for the club three weeks ago in the defeat at York, while Goodison hasn't played for five weeks due to a thigh injury. He is supposed to be returning to training soon, and should be available for the games at Rochdale and Swansea next week.