Hicks released a statement on Sunday evening in which he described the latest report as "a complete fabrication and ... absolutely and categorically untrue".
"Whoever is behind this false report, the facts are that I and my family have always been, and remain, fully committed to co-owning the club; that no-one in my family has ever indicated any intention or desire to sell our stake in the club; and that we expect and intend to be co-owners of the club, and to actively and enthusiastically support the club's manager, players and fans for many years to come."
Hicks' statement was released through financial and corporate communications consultancy FD.
Reports had claimed on Saturday that DIC were set to make an offer for the complete buy-out of the American duo.
The Dubai-based group were close to their own takeover of the Anfield club 12 months ago before the Reds' then chairman David Moores decided to go with the USA investors.
On Thursday a spokesman for Hicks insisted neither of the owners was considering selling their share and both remained fully committed to the club.