Mayor Lee Leffingwell and two other City Council members said they would propose the ban Monday, the Austin American-Statesman reported.
The plastic bags pollute waterways, harm wildlife, clog drainage systems and take up landfill space, Leffingwell said.
"I think there will be a cost benefit and a benefit to the environment of going down this road and coming up with a reasonable ordinance" to end their use, Leffingwell said.
Austin's Solid Waste Services Department said city residents use 263 million plastic bags a year and the city spends $850,000 annually on cleanup and disposal.
The City Council will vote Aug. 4 on the resolution from Leffingwell and Council Members Mike Martinez and Chris Riley.
If the proposal passes, the city would determine a scope for the ban and a timetable for gradually phasing it in.
"I'm sure many retailers have a lot of plastic bags on hand or [long-term] contracts with bag companies. We want to take those things into consideration," Leffingwell said. "Our goal will be to develop a reasonable ordinance that doesn't cause hardship. It would be a hardship to enact a ban immediately."