Assem and son, Ehab, recently completed their £40m takeover of the Championship club and are now keen to purchase the 25,000-seater stadium.
"We have not yet had chance to get stuck into the 'nitty gritty' details, but that is our aspiration," said Ehab.
"We do not know if the council are prepared to sell," he added.
Should the duo manage to buy the ground it is believed the would hope to increase the capacity to 38,000.
Hull City Council leader Carl Minns says they would agree to discuss the matter further with the Eqyptian businessmen.
"The Allams are very serious players in the area. Of course we will listen to what they have to say."
Source: BBC Sport