The Football Association rejected a proposal pushed forward by the Egyptian in April to change the club's name to Hull Tigers, with no appeal process.
Allam vowed to sell Hull if he was unsuccessful in his bid, and followed that through with an announcement on Thursday.
He also revealed that he had started appeal proceedings to the Court of Arbitration for Sport, and suggested he would remain if that appeal was successful, but also hinted interest in purchasing the club had been lodged.
"Until the conclusion of the appeal or the sale, whichever comes first we will remain fully committed to the club," he said at a news conference.
"If the appeal comes first, no harm done. If the sale comes first, sold.
"If I sell, I would like to make sure the club is moving to a good home. Better than mine.
"We stated earlier this year, that the club would be for sale should our attempt to globally promote Hull Tigers as a brand name and as a playing name be blocked. As a consequence of the FA decision on 9 April I announced on 10 April, within 22 hours, that Hull City is for sale."
Allam remained tight-lipped on the identity of any potential investors and, when asked what the outcome would be if no offers for the club were received and his name-change appeal being rejected, claimed he would "give it away".
