Imps chairman Steff Wright admitted it "was unlikely" the club will be able to reach agreement with the duo.
"Adrian has rejected his contract and the deadline that was set to reach an agreement [Tuesday] has since come and gone," Wright told the Lincolnshire Echo. "The consequence of that is we now have the power to withdraw the offer altogether.
"The ball is back in our court now with respect to his future and Peter must decide whether he is willing to sit down at the negotiating table again.
"I know the question that is bound to be asked is 'will he be here next season?' I would say at this stage that looks unlikely because the player may have his eye on moving somewhere else."
On Mullarkey, Wright added: "Sam has reject his contract and, similar to Adrian, it will be down to Peter to decide whether he wants to sit down and negotiate with him again."