Sky News understands that Foxtons is in exclusive negotiations to acquire the privately owned chain, which has about 18 branches in the capital.
A property industry source said the deal was likely to cost Foxtons in the region of £15m, making it a small-but-significant deal by industry standards.
Foxtons has recovered more robustly than originally anticipated since the start of the COVID-19 crisis, telling investors in December that it was increasing its full-year profit forecast.
Last year, it raised more than £20m from shareholders in a placing after warning of a collapse in revenues.
In recent weeks, rumours have circulated about a potential private equity bid for Foxtons, although it was unclear on Monday whether that speculation was credible.
While its shares remain 30% lower than this time last year, they are now worth more than double the 31.5p they slumped to last May.
Douglas & Gordon, which is family-owned, is run by James Evans, a former Foxtons executive.
It is understood to have held talks with a number of parties about a full or partial sale in recent months.
Neither Foxtons nor Douglas & Gordon could be reached for comment.