It is testing the campaign via its customer market research panel, Sainsbury's Team, which will encourage shoppers to test its prices against Safeway.
It reads: 'Go on: ask Safeway if they've got all this', and highlights £5 discounts, half-price strawberries, and a petrol offer of up to 4p off a litre.
Sainsbury's slipped to third spot in the supermarket sector last year, with a market share of 16.2%, behind Tesco (27.6%) and Asda (17%). The Morrisons-Safeway merger in March created a market share of 14.2%.