The move comes after Monarch’s administrators KPMG won an appeal last week, giving it the rights to sell the lucrative Luton and Gatwick slots.
KPMG is hoping to use the sale of the slots to recover some of the £466 million owed.
Reuters reported a source as saying "we’ve expressed an interest” , confirming that Cook had bid for slots at Gatwick but not at Luton, although Thomas Cook Airlines declined to comment.