The 75-year-old held a press conference this afternoon to explain that there has been interest in the club, but would prefer to remain as owner should an appeal against the Football Association be successful.
The club are attempting to overturn the FA's refusal to permit a name-change by going through the Court of Arbitration for Sport.
Allam told reporters: "Lately there have been a lot of rumours and that is not a good thing so I decided it was better to have a face-to-face conference and clear the air.
"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 April 9 I announced on April 10, within 22 hours, that Hull City is for sale."
The English governing body rejected Hull's plans to change the club's name back in April.