Councillors have discussed plans aimed at improving the city's transport network and changing its image as what a report calls a "motorway city".
City Square could be closed off to through traffic by 2021, as could Neville Street that runs past Bridgewater Place into the city centre.
The move forms part of the city's 2023 European Capital of Culture bid.
The plan was to get more people cycling and walking around the city, the report said.
Cycles, buses and taxis would still be allowed in City Square that lies close to the railway station.
Councillor Richard Lewis said: "It's about how me make the city both liveable and prosperous in the future."
An upgrade of Armley Gyratory, one of the busiest junctions in the city, was also in the council's plans, he said.
There were still many details to be worked out and there would be feasibility studies and consultations, Mr Lewis added.
The plans are part of a discussion on a 20-year vision for the city.
The HS2 high-speed rail network is planned to stop at a new city centre station in Leeds by 2032/33.
The council must register its capital of culture interest by December 2016 and submit a final bid in 2017. The winning bid is expected to be announced in 2018.
Parts of Leeds city centre could be closed to traffic in a bid to make the city less "road heavy".