The combination would create a retail giant worth between £11 billion and £13 billion (€12.5 billion to €14.8 billion) which would have more than 581 supermarkets, 700 petrol forecourts and 100 convenience stores in Britain, the newspaper said.
Zuber and Mohsin Issa
Asda and TDR Capital declined to comment.
The Issa brothers could not immediately be reached for comment.
Talks over merging the two businesses come ahead of a refinancing of EG Group, which has £7 billion (€7.97 billion) of debt due in 2025, according to the report.
Last week, Britain's competition regulator said it has begun investigating British supermarket group Asda Stores' purchase of Co-Operative Group's petrol forecourt estate.
The Competition and Markets Authority (CMA) said it had until March 14 to make its phase 1 decision on whether the deal will reduce competition in the UK.
Asda is planning to open 300 convenience stores by the end of 2026, aiming to become a player in the smaller shop market to help drive growth, and creating thousands of new jobs in the process.
The supermarket group had agreed to buy Arthur Foodstores Ltd, which comprises of 129 sites, from Co-Operative for £600 million (€683.4 million) in August last year.
Asda and Co-Operative did not immediately respond to Reuters requests for comment.