The group, which has more than 100 cafes, has brought in KPMG to advise on its options.
It comes in the midst of an increasingly tough trading environment, with a growing number of operators closing sites in the face of rising food costs and business rates.
Last month creditors at the Byron burger chain voted in favour of a company voluntary agreement (CVA) that could see up to 20 restaurants shut.
The 300-strong Prezzo chain has also appointed consultants at turnaround firm Alix Partners to advise on its options.
A spokesperson for Eat told Sky News it was not working on a CVA, though Sky reports the chain is likely to press ahead with plans to close a number of stores.
Eat is majority owned by private equity firm Lyceum Capital, which backed a buyout of the chain in 2011.
Despite headwinds hitting the eating out sector, Eat continues to be profitable. The group reported a 5% growth in like-for-like sales in the year to June 2017, with adjusted earnings up 19% to £4.3m.