Sainsbury's is said to be eyeing a number of Kwik Save's recently closed stores with a view to bringing them under its Sainsbury's Local fascia.
"Sainsbury's is looking to expand its convenience store business, and some of Kwik Save's smaller outlets would definitely be a good fit," a source close to the retailer told C-Store.
Last month Sainsbury's chief executive Justin King announced that he was planning to grow Sainsbury's convenience business by 30% in the next three years - boosting its portfolio to 426 stores.
Last week Kwik Save was forced to close 79 of its stores across the country in a dramatic bid for survival.
Neither Sainsbury's nor Kwik Save would comment on the claims.
Meanwhile, Tesco has revealed plans to renovate just under half of all stores in its One Stop convenience chain by the end of this year.