Allam has attracted fierce criticism from some supporters after going public with his desire to rebrand the club as 'Hull Tigers' following their promotion to the Premier League in May.
The Egyptian-born businessman - who took over at the KC Stadium in December 2010 - claims doing so would help maximise the club's commercial potential, but groups of fans have responded to this proposal by unfurling banners reading 'City Till We Die' and 'We Are Hull City' at home games.
Allam has slammed this campaign, saying those responsible are undermining manager Steve Bruce's efforts to keep the side in the top flight while insisting he would have no hesitation in selling the club if most fans are not supportive of his ideas.
"They (the City Till We Die campaigners) can die as soon as they want, as long as they leave the club for the majority who just want to watch good football," he told the Independent on Sunday.
"How can you be supporting a club when you distract attention during a game?
"I'm a simple man. Do they want me to stay? If it's 'no thank you', fine, in 24 hours the club is for sale... I do not put in one more pound."
Hull will look to bounce back from a first home defeat of the season, against Crystal Palace, when they host Liverpool on Sunday.
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