Shares in the UK's second-largest supermarket rose 2.5% after reports it had made a bid of Â£130m for the chain, which has 3,000 stores.
That made Sainsbury's the biggest riser on the benchmark FTSE 100 share index, which was up 41.07 points, to 0.6%, at 7,504.61 shortly after midday.
In the FTSE 250, Ocado jumped 8.6% on talk that it could become a bid target.
Credit Suisse said last week's announcement that Amazon was buying Whole Foods increased the likelihood of Ocado being a takeover target. Separately, analysts at Exane raised their rating on Ocado to "outperform".
Shares in womenswear chain Bonmarche fell 2.6% after it reported a 40% fall in annual profits.
The retailer admitted that the past year had been "more challenging than we had expected", with the market hit by a combination of rising prices and wages, uncertainty surrounding the Brexit referendum, and unseasonal weather.
On the currency markets, the pound rose 0.2% against the dollar to $1.2796 and was 0.1% higher against the euro at 1.1428 euros.
Sainsbury's led the UK's stock market higher amid reports it is in talks to buy convenience store chain Nisa.