The plan is being considered as part of attempts for the authority to save £80 million in the next three years.
The council is responsible for 24 sites in the county, including Meole Brace Golf Course.
In 2012, Serco was brought in by the council to help manage five leisure centres – Shrewsbury's Quarry Swimming and Fitness Centre; Shrewsbury Sports Village and Indoor Bowls Hall; Whitchurch Swimming Pool; Market Drayton Leisure Centre; and Oswestry Leisure Centre.
An organisation called the Shropshire Community Leisure Trust set up to help run the facilities, with Serco as the managing agent to the trust. The contract, which started in August 2012, is running for an initial 10 years, with an option to extend it for a further five.
It is now intended that the running of the council's other leisure centres will be put out to tender, although the buildings will remain in council ownership.
It is hoped the change could save more than £550,000 for the council.
A total of £118,000 is earmarked to be saved next year through the review of leisure facilities, more than £205,000 in 2015/16 and over £225,000 in 2016/17.
James Walton, head of finance for Shropshire Council, said the model used for the five centres under the control of the leisure trust could now be rolled out to more facilities.
"There were a number of leisure centres that we moved out to Serco and are being delivered by that contract," he said. "There are a number of leisure centres that weren't part of that before."
He said the council strategy would now be to look at moving onto changing the management of those centres.
The changes are part of attempts by Shropshire Council to review and redesign all of its services to meet its £80 million funding gap for the next three years.
On Saturday it was revealed that the council is looking at compulsory redundancies in a bid to shed around 1,700 jobs. Other changes under consideration include potential library closures and cuts to transport services.
Teme Leisure also runs several centres in Shropshire on behalf of the council, including facilities in Wem, Church Stretton and Cleobury.
Among the facilities that are currently council-run and could be affected by the changes are Bridgnorth Leisure Centre, Lakelands Centre in Ellesmere and Rhyn Park Sports Hall near Oswestry.