Epiris, whose current investments include the auction house Bonhams, is understood to have emerged in recent days as a front runner to buy the Cafe Rouge and Las Iguanas operator, according to Sky News.
A deal could be struck in the coming days, with other bidders, including activist hedge fund Elliott Advisers, understood to have also lodged an interest in buying CDG.
The restaurant group, which also owns Bella Italia, fell into administration at the start of this month with 91 sites in its 250-strong restaurant estate set to be closed permanently, a move that will put 1,900 jobs of its 6,000-strong workforce at risk.
Other investors have tabled bids for individual brands within CDG, although Epiris is now said to be the leading contender to buy the whole group.
The private equity firm had also made an offer for Azzurri, the owner of high street casual dining brands Ask Italian and Zizzi as well as the faster casual Coco di Mama, but appears to have lost out on the deal to Towerbrook Capital Partners.
AlixPartners is overseeing CDG’s insolvency process.