According to a report in The Times, the 14-strong business has been working with advisers at BDO for the past few months to find a new owner.
Johnson is one of the hospitality sector’s most prominent entrepreneurs, having built some of the UK’s best-known high street brands.
He is best known for expanding Pizza Express during the 1990s, growing the business from a relatively small chain to more than 250 restaurants.
Other businesses he has been involved with include Signature Restaurants, which at the time owned The Ivy, Le Caprice, J. Sheekey and Belgo, as well as Strada, Gail’s, Patisserie Valerie, Gaucho, Giraffe and Feng Sushi.
Talks are understood to be ongoing with Wahaca, which was founded in 2006 by Thomasina Miers and Mark Selby and has grown to become the UK’s largest Mexican casual dining brand.
Founded in Covent Garden, Wahaca peaked at almost 30 restaurants in the early 2010s but has since reduced its estate.
The business is a pioneer of authentic Mexican food in the UK and a move away from the heavy Tex-Mex clichés that dominated the market during the 1990s.
It was also an early pioneer of street food-inspired dishes and played a significant role in popularising Mexican drinking culture through its focus on agave-based spirits.
Wahaca has also been recognised as a leader in sustainability. More than half of its menu is entirely meat-free, while the business removed steak from its menu to reduce its carbon footprint and became one of the first UK restaurant groups to print carbon counts alongside calorie information for every dish.
Earlier this year, Wahaca appointed retail, leisure and placemaking agency P-Three to source new sites as it looked to return to growth.
P-Three is targeting sites of approximately 2,500 to 4,500sq ft in areas such as Cambridge, Manchester, Glasgow and Birmingham.
Wahaca is also looking to further expand its footprint in London with sites in Marylebone, Baker Street, Victoria, London Bridge and King’s Cross.