The Ibrox club have already had staggered offers of £400,000 and £750,000 turned down but several Sunday newspapers claimed a deal was close to completion after Rangers submitted a third offer.
However, it has emerged that the bid, £750,000 up front, possibly rising to £1.5million, has been kicked out by the Ayrshire club.
Rugby Park boss Jim Jefferies told the Sunday Herald: "There is probably a fee that the club couldn't turn down, but Rangers are nowhere near it, and if they keep coming back with add-ons and things like that it just isn't going to happen."
Chairman Michael Johnston told BBC Scotland: "We've given them an indication of the kind of figure that would make us think about selling.
"So far, they haven't come near that. Therefore, we're a long way from reaching an agreement."