On Thursday, Alison Johnstone will ask the council to roll out a scheme where shops offer canvas bags that also act as a customer loyalty card, according to the Guardian.
Shops in Leith, Marchmont, Sciennes, Tollcross and Bruntsfield already run a scheme that rewards customers for reusing the bags.
Johnstone has teamed up with Gordon Millar who is driving the campaign and runs the Ban Plastic Bags Edinburgh campaign.
The campaign comes after plastics packaging bodies supported a legal challenge against a ban on plastic bags in Italy that is said to contravene European law.
The Welsh government is set to introduce a levy on carrier bags from October.