Clapham House is understood to be in exclusive talks with Urban Dining to buy its 30 Tootsies burger and grill restaurants.
Both Clapham House (which operates the Real Greek, Bombay Bicycle Club and Gourmet Burger Kitchen chains) and Urban Dining declined to comment.
However, analysts believe the two are seeking to hammer out a sale within the next week or so. The deal is expected to value the company at more than £25m.
Any failure to agree a speedy sale would open the way for other potential buyers - such as Giraffe, PizzaExpress and Ask owner Gondola Holdings, or Strada - to return to the negotiating table.
Clapham House is expected to raise the cash for the deal through a share placing with institutional investors, which will be announced soon.
Urban Dining bought Tootsies for £30.6m in 2004 as the first in a planned three-brand line-up, but decided to cut its losses in December in the wake of poor trading results.
Its restaurants, which are mostly leasehold properties, are a mix of high-street and concession-style sites.
By Angela Frewin