Sources said that the talks were several weeks from being concluded and that a deal was expected to place an enterprise value on D&D of about £100m.
LDC, the private equity arm of Lloyds Banking Group, has owned a majority share in the business since 2013.
A deal would represent a bet on the recovery of central London's fine dining scene in the wake of the pandemic.
Interpath Advisory, the former restructuring unit of KPMG UK, has been advising on the sale of D&D as it widens its offering into the provision of general corporate finance advice, according to people close to the process.
The exact structure of Montecito's acquisition of D&D is reportedly unclear, but one insider told Sky News it was possible that LDC would retain a small stake in the business.
D&D London was originally founded by restaurateur Sir Terence Conran as Conran Restaurants, and changed its name in 2006 current chairman Des Gunewardena and deputy chairman David Loewi took a controlling stake.
The group owns prominent London restaurants including Bluebird in Chelsea, Coq d’Argent in the heart of the City, and Skylon on the South Bank