It follows an unsuccessful partnership with Chinese company ofo, which had reached a deal to provide such a service in 2017, before withdrawing at the eleventh hour.
The authority now claims it is speaking to 11 other companies to kickstart the scheme, with councillors claiming mistakes made on similar schemes in Manchester and Sheffield.
The scheme would mean that anyone wanting to travel quickly around the city centre could rent a council-owned bike from a docking station for a period of time. They would then deposit the bike at a drop off point near their destination.
Council head of transport and planning Richard Lewis said: “We went back to the drawing board.
“I think we will have a lot of interest – with the number of firms coming in who could fulfil this role, we will have a choice.”
The scheme could be similar to the bike hire service in London introduced in 2010, where card details are entered into a docking station and payment is measured by the time the bike is in use.
But Conservatives group leader Coun Alan Lamb made allusions to bike schemes in Sheffield and Manchester, which saw incidents of hired bikes left in gardens and canals.
He said: “There are cycling cynics, and I am not one of them.
“But we need to get reassurances on recovery of the bikes and that they are not going to be littered around communities.”
Coun Lewis responded: “Other cities like Sheffield and Manchester have faced this. But this is a scheme where you know exactly where they are the whole time, and if someone does throw a bike in the river, they will have to pay for it.”
Liberal Democrat group leader It could be similar to the bike hire scheme in London introduced in 2010, where card details are entered into a docking station and payment is measured by the time the bike is in use.
Coun Stewart Golton echoed Coun Lewis, adding: “I read the report with one eyebrow raised because of other bike share schemes.
“We have come to this late on, which means we may have learned from some of the mistakes from other cities.”
The council report stated: “There is a strong and still growing market for bike share in the UK, and a renewed interest for working in Leeds. The current models are considered to be have the more robust commercial and operating models that may be expected from a maturing business sector.
“Leeds is seen by bike operators as a significant market for their services and many key players in the industry are keen to establish a scheme in the city.
“This offers an attractive opportunity for a bike share scheme that is appropriate to the needs and aspirations of the city which will underpin the “Cycling Starts Here Strategy” for growing cycle use and contribute to the vitality of the city.”
Approval has now been given to formally tender the scheme and seek a company to run the service.