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.

Striker Robson-Kanu, 27, who is expected to be part of Wales' squad for the European Championships, has spent seven seasons with the club.
Former West Ham and Sunderland defender Ferdinand, 31, has suffered with injuries in two seasons at Reading.
Academy graduate Cox, 29, who rejoined the club in summer 2014, has struggled for goals in the last two campaigns.
The Championship club have also confirmed that six loan players who represented them this season have all returned to their parent clubs.
Defender Andrew Taylor, midfielders Ola John and Alex Fernandez and striker Matej Vydra follow the departures of Chelsea pair Michael Hector and Lucas Piazon, who left the club last month.

At least 80 people were killed during the attack on the 1,500-seat venue during a sell-out gig by US rock group Eagles of Death Metal.
University of Nottingham student Hanna Corbett said there was blood all around and people lying on top of each other.
The student, originally from St Albans, said she thought she and her friend were about to die.
She said people inside did not realise straight away what was happening.
"It sounded like fireworks or firecrackers and it wasn't until people started screaming and the lead singer ran off stage [that people knew something was wrong].
"The lights went on and everyone just dropped to the floor," the 21-year-old history student said.
"There was blood all around and people were hugging each other."
Describing laying on the floor, with the gunmen on the balcony, Ms Corbett said: "It felt like ages but it could have been just five to 10 minutes - there was this banging which seemed like a real gun - I'd never heard one before.
"[People were] crawling over each other, just trying to climb out of fire exits. It was pretty inhumane - a nightmare.
"I thought it was like that heroic thing on the train," when a suspected radical Islamist was overcome by six passengers.
"I thought someone would just stop them - but the guns kept going and I thought 'this is the end'."
Ms Corbett said luckily she and her friend Jack Konda, 21, also a student in Nottingham, managed to get out.
He said: "We were dealt a pretty lucky hand to have been so close to it and get out pretty much unscathed."
A French journalist captured the horror of people fleeing from gunmen who stormed the venue.
Le Monde newspaper reporter Daniel Psenny was himself shot as he tried to help a man who collapsed on the pavement outside.
Parts of Leeds city centre could be closed to traffic in a bid to make the city less "road heavy".
[NEXT_CONCEPT]
Reading are to release Hal Robson-Kanu, Anton Ferdinand and Simon Cox after their current contracts expired.
[NEXT_CONCEPT]
A student has spoken of the "nightmare" of being caught up in the attack on the Bataclan concert hall in Paris.