The Daily Telegraph says the Dubai government-run fund admits it would be prepared to accept a 49 percent stake in the English Premier League club.
Hicks made the partnership proposal nine days ago in a 60-page shareholder agreement e-mailed to DIC's lead negotiator Amanda Staveley.
Staveley, a senior partner at DIC's advisers, private equity firm PCP Capital Partners, was quoted as saying on Friday: "Subject to renegotiation of a partnership agreement and subject to the usual stringent minority shareholder protection rights we would be prepared to accept a 49 percent shareholding in Liverpool FC.
"We have decided that this arrangement provides the best possible solution to the situation and would be in the best interests of the club and their loyal fans."
Under the terms of the deal, which the Telegraph said would be discussed by senior officials from both sides in Dubai next week, DIC would buy 49 percent of the shares from Gillett and Hicks would buy one percent giving him a 51 percent stake.