Shropshire Council's plans for a revamped facility were approved by the authority's cabinet earlier this month.
As part of the process the plan needs to be formally approved by the full council, which meets on Thursday.
It is hoped that the building work will start in 2024 and be finished the next year.
The new premises, which would be built on the site of the old pool, will include a new pool, rooms, a gym and a café.
The current pool at Whitchurch has been closed since March 2020.
The project had initially been expected to cost between £7m and £8m, but had risen to more than £13.1m – partly due to inflation and increased construction costs.
Other fresh swimming pool projects have been dropped by the council, with plans for a replacement pool at Shrewsbury's Quarry Fitness Centre and a fresh facility at Shrewsbury Sports Village in Sundorne both cancelled.
Speaking when the Whitchurch project was confirmed in March, Council leader Lezley Picton said the rising costs had left the authority with no option but to go back to the drawing board on the Shrewsbury projects.
The Whitchurch plans include the construction of a brand new swimming centre featuring a six-lane 25m pool with a movable floor, a 35-station fitness suite, multi-function rooms and a café with 20 covers.
Shropshire Council said the site had been unable to reopen since its 2020 closure after investigations discovered that work to fix a leak in the pool would be more difficult than expected.
A consultation on the plans for the new facility had 286 respondents, with 89 per cent agreeing with the location, and 73 per cent agreeing that the proposed facility mix was adequate.
The council will be asked to vote for including £13.1m for the project in its capital programme, and to delegate to the executive director of place, in consultation with the portfolio holder for communities, culture, leisure & tourism, to procure, negotiate and agree the terms of any agreements and contracts necessary.