As highlighted by MEATliquor founder Scott Collins on Instagram, Lina Stores put in a premises license application to Lambeth Council for 15 and 16 The Pavement, London, earlier this month.
According to the application, Lina Stores intends to operate both a restaurant and retail space, with the latter expected to be situated in the smaller Counter Culture space.
It will be the third London restaurant for the group.
Lina Stores started out life as a deli on Brewer Street in Soho back in 1944, and only moved into the restaurant space in the last five years after securing finances from venture capital business White Rabbit Projects and appointing chef Masha Rener to help develop the menu.
The group's first restaurant opened on Greek Street in Soho in 2018, and was followed just over a year later with a huge second site in King's Cross.
Last month Lina Stores launched its first overseas location in Tokyo.
It is also understood to be considering further openings in the capital.
Gill permanently closed both The Dairy and Counter Culture last year as a result of the Covid-19 pandemic, but subsequently relaunched the former in Bermond Locke under the name Bermondsey Larder.
Opened in 2013, The Dairy was a cult hit and an early proponent of a more laid-back, rustic and affordable approach to fine dining.