Le Riche, which runs 45 stores in Jersey and Guernsey, is now part of trading conglomerate CI Traders, but still effectively run as a separate business.
Analysts said a move into the Channel Islands would not be beyond the realms of possibility for Tesco, which has distribution centres on the south coast and has made no secret of its ambition to boost its convenience store estate.
Any deal would also be unlikely to raise competition issues as the Office of Fair Trading’s remit does not cover the Channel Islands, said a spokesman.
CI Traders’ chief exective Martin Bralsford said he had not scheduled any meetings with Tesco.
He added that Morrisons appeared keen to hang on to the two Safeway stores located on the islands.