The governing body spoke out at the end of a day which had seen numerous reports suggest Allam's idea to rebrand the club as Hull Tigers was set to be quashed.
In a statement, the FA said that, at a meeting last Wednesday, its membership committee had made the recommendation to the council after "consultation with stakeholders within and outside of the game".
The statement added that a full vote would be taken as planned on April 9 and that Hull were able to respond with a new submission, having been sent the written reasons.
Allam later told the Guardian that he would walk away from Hull if his plan failed, but moved to deny he would liquidate the club.
While also admitting he would now ask Hull's season-ticket holders to vote on the issue, he said: "We will announce a ballot this week, and we will challenge the decision.
"If the FA does not allow our plan, we will walk away, put it on the market to sell the club. We would not put it into liquidation; there is a lot of money at stake. I will get my money when I sell."
His quest to rebrand the club met with a furious response from fans' groups and led to a war of words with Allam.
The Football Supporters' Federation hailed the reports on Monday and praised the campaign waged by the club's supporters.
FSF chief executive Kevin Miles said: "This is undoubtedly the right decision and credit should go both to the FA and to Hull City fans, who led a tremendous campaign.
"The fans' groups and fanzines who came together under the City Till We Die banner have protected their club's heritage and 110-year-old name with great dignity.
"The FA's decision should also serve as a warning to other owners - such fundamental changes to a club's identity should not be made without the support of the fans."
Allam's son, vice-chairman Ehab Allam, said at the weekend that a formal rejection by the FA would not stop him pushing for the change in the long term.
Ehab Allam told BBC Radio Humberside: "The proposed name change is not about a quick win. It is a long-term change."
His was perhaps a voice of reason between the fans and the club, with his father having previously stirred passions further by telling the fans who sung the 'City Til I Die' song that they could "die as soon as they want".
- Sports & Recreation