The club have been up for sale since 2014, after the Football Association turned down owner Assem Allam's request to a change of name to Hull Tigers.
As offer is now understood to have been made and talks held over the weekend have been described as "constructive".
Hull face Derby in the second leg of their play-off semi-final on Tuesday, having won the first game 3-0.
In May 2015, Egyptian Allam told BBC Look North he had rejected offers for the club as he wishes to ensure it goes to a "good home".
Allam took charge of the Tigers in December 2010 and they were subsequently promoted back to the Premier League under manager Steve Bruce, before relegation last May.
Talks have begun about a possible takeover of Championship side Hull City, reports BBC Radio Humberside.