The group is understood to be in discussions with Patty & Bun to take over the 26 Kingly Street location.
Breddos says in a statement: "We can confirm we are reviewing our plans for Kingly Street. We are in advanced conversations with Patty & Bun, but no final transaction has been completed. Breddos Goswell Road, the original site, will continue to be open."
If the deal goes through the restaurant will be Patty & Bun's tenth overall location.
Breddos started out as a makeshift taco shack in a car park in Hackney in 2011, before launching bricks and mortar sites in Clerkenwell in 2016 and Soho in October 2017.
The reason behind the closure of Soho is not known, but the Breddos team is opening a joint Mexican restaurant project in Liverpool in November following a sell-out pop-up in the city.
The Soho site was previously home to US chef Brad McDonald's short-lived Shotgun Barbecue restaurant.
Breddos is part of a joint venture with The Hoxton and Gleneagles owner Ennismore.