Moorways was closed to the public in 2016 but continued to be used by swimming clubs until the end of January.
The decision was made in a bid to save about £350,000 a year.
Council leader Ranjit Banwait said that whatever the cost of a new pool, it was important to get it right.
Moorways, built more than 40 years ago, has struggled with maintenance and health and safety issues.
Derby's other big pool, at the Queen's Leisure Centre, is currently closed due to structural problems, although two other pools remain open for public use at the centre.
The Moorways closure was opposed by high-profile swimmers Ross Davenport, who won two gold medals at the Commonwealth Games in 2006, and Olympic champion Adam Peaty, who now trains outside the city.
Mr Banwait said: "To start work on the pool we've set £20m aside as an initial amount of money.
"Potentially the work is going to cost more than that, we are currently looking at the designs... if it means it is going to cost more we will put that money in place.
"The most important thing is that we get this right, this pool's going to be built and it's going to be there for generations to come."
The new 50m pool is expected to be built by 2020.
A replacement for one of Derby's council-run swimming pools could cost more than the £20m the local authority estimated.