The right to ask for flexible working already exists, but staff have to be in their jobs for six months before they can do so.
The new proposal, for which a consultation has been launched, is that they should have the right to request it from day one of their employment.
ACS chief executive James Lowman said: “We know how important it is to our colleagues to balance to work and personal commitments so we welcome more clarity on flexible working requests.
“The convenience sectors offer genuinely flexible, secure working opportunities that are informed by good communications between retailers and stores colleagues.”