Leeds have rejected two separate bids for the striker this month and the player has now made an attempt to force the issue by formally requesting a transfer.
Manager Neil Warnock revealed recently that he hoped Becchio would stay, but the club has admitted that it will entertain "acceptable" bids.
A club statement read: Luciano Becchio, who has been the subject of two separate bids from foreign clubs during the January transfer window, has handed in a transfer request to the club, as financially he believes his best interests are served by a move away from Leeds United.
"The club have sought to agree the terms of a new contract with the player, who is already the highest earner, but the requested terms were beyond a level that we could support, particularly in view of the regulations relating to Financial Fair Play that will be effective in coming seasons."
Becchio has scored 76 league goals since joining Leeds in 2008.