The Egyptian-born businessman is trying to change the Lancashire outfit's name to Hull Tigers in an attempt to maximise global commercial opportunities.
However, the FA have announced that its membership committee expect to reject the request when a full vote is taken on April 9, leading to Allam again issuing his ultimatum to walk away if the name change is not implemented.
While also revealing that he would now ask Hull's season ticket holders to vote on the issue, he told reporters: "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."
Allam took over at the KC Stadium in November 2010.