A review carried out by the local authority has proposed building two "modern new centres" in place of the city's Central and Arthur Hill pools.
The council said it would need to spend £10m on maintaining and repairing the two "outdated" facilities.
A temporary pool could be set up at Rivermead Leisure Centre while the Central Pool replacement is built.
The new Central facility would be an eight-lane, 25-metre competition swimming pool that would be ready in about four to five years.
It would include diving facilities and a new five-court sports hall to host a range of indoor sports.
The 25-metre temporary pool could open within two years, include a learner pool and have a lifespan of at least five years.
A feasibility study would also be carried out to create a six-lane 25-metre pool at Palmer Park, linked to existing leisure facilities.
Paul Gittings, the council's lead member for sport, said the plan was "the most cost-effective way" to deliver high-quality swimming facilities.
He added: "It makes no sense to continue to pour money in outdated facilities in order to keep them going for a limited period of time."
The Central Pool is scheduled to shut  from 7 December to 21 December for maintenance work.
The plans will be considered at the next meeting of the council's Policy Committee on 30 November.
Two ageing Reading swimming pools could be replaced in £25m plans announced by the borough council.