The group - which was crowned London Pizza Festival champion in September - has made an offer on a 35-40 cover site, which it hopes to open in June.
Co-founder Ed Sandeman told BigHospitality he was holding off on announcing the exact location until the sale had gone through.
The restaurant will keep a ‘tight’ pizza menu with just five or six options, but will have an extended sides menu, wine list, and serve a selection of prosecco, cocktails and beer.
Sandeman said: “If you go in to a traditional pizzeria there are about 30 different pizzas on the menu and often that means that the produce isn’t that good. So our focus is using the best ingredients we can but on a shorter menu.”
The restaurant design will focus on the 'theatre' of pizza-making, with an open kitchen, two long sharing tables and a bar surrounding a wood-fired oven.
“Everyone loves watching chefs make pizza, with the smoke and the noise, it’s more of a show than just a [sit-down] meal,” said Sandeman. “We wanted to bring that in to the restaurant, so the oven is going to be bang in the middle.”
It is hoped that the new restaurant will be a community space used to host events and workshops during the day.
Made of Dough was created by Sandeman and his friends Henry Amodio and Harry Gibson in 2014, with the trio opening in Pop Brixton in May 2015.
It serves ‘proper Neopolitan pizza’ with selected ingredients sourced from southern Spain.
Varieties include the Obrasada - topped with organic majorcan cured pork, friarielli, red onion & fior di latte - and new dessert pizza Conchiglia a Nutella, which fills warm folded dough with Nutella and hazelnut.
The next few months are set to be a busy time for the team, who will begin a six week residency at Market Yard in Shepherds Bush from Wednesday until 1 May.
They are also set to launch a three month pop-up in a converted shipping container on the South Bank from 6 April.