DIC lost the race to buy the club last year but Gillett is reportedly keen to sell his stake to the group.
Gillett and Hicks are in the middle of a bitter power struggle.
The American duo took control of Liverpool in a deal worth £218.9m in February 2007 but the relationship between the two men broke down some time ago, with the pair no longer on speaking terms.
Their falling-out has led to a war of words breaking out in the Anfield boardroom and in a television interview last week, Hicks defiantly outlined his own plans for the future of the club as well again calling for Parry's resignation and claiming the chief executive's tenure was a "disaster".
Gillett, an ally of Parry, responded by saying he would not sell his stake to Hicks and by inviting DIC to the first leg of the European showdown with Chelsea, he has made a clear statement of intent.
DIC has been trying to buy the club for 18 months, having been beaten by Hicks and Gillett just over a year ago.
The investment group seemed to have tied up a deal at the turn of the year, only for Hicks to send a representative to Dubai for talks before pulling the plug on the possible sale.
After the Chelsea game, Liverpool boss rafael Benitez revealed that he had spoken to Hicks ahead of the game.
He said the pair discussed the possibility of a meeting of all parties regarding the future of the club's ownership and direction.
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