It is set to apply to Croydon Council in south London for permission to increase its Purley Extra from 82,000 sq ft to 139,000 sq ft. Tesco's largest supermarket at the moment is a 119,ooo sq ft Extra in Newcastle-upon-Tyne.
Asda has a 110,000 sq ft site in Milton Keynes while Sainsbury's biggest store is its 87,ooo sq ft London Colney store in St Albans.
"We want to improve the customer offering at Purley by expanding non food," said a Tesco spokesman. "Plans also incorporate a community square area for people to enjoy. We look forward to working with the community to enhance Purley centre."
Croydon councillor Tim Pollard said if expansion of the store became "inevitable" then the council would ensure benefits were ploughed back into Purley through planning gains, by which retailers build other amenities such as homes.
"We have potential to gain significantly from this expansion in terms of new facilities in Purley. I will be making sure we will fully exploit it."
The retailer also has outline planning permission to open another supermarket in the borough, having been chosen as Croydon Council's development partner for the multi-million pound renewal of Central Parade in New Addington. Here, Tesco will provide 300 new homes, a community building with sports hall, swimming pool and other facilities. Work is set to start next April, subject to permission.
Demands for extensive planning gains in exchange for permission to build new stores is a growing trend, said Jonathan Pritchard, retail analyst at Oriel Securities. "It sounds as if Tesco will have a particularly good market share in this part of London, so it may be the council can make higher demands."
Tesco has 42% of the Croydon postcode market share now, according to retail consultancy CACI, with Sainsbury's on 31% and Asda on 6%.