At least eight countries had expressed some interest in wanting to host the sport's showcase event but just three candidates remain in contention: Doha (Qatar), Fukuoka (Japan), and Nanjing (China).
FINA will vote to decide which two will host the 2021 and 2023 championships at a meeting in Dubai on November 8.
"We have three for the moment, definitely three," FINA executive director Cornel Marculescu told Reuters on Friday.
"Nanjing, Fukuoka and Doha are the bidders. This is the finished deadline."
Australia and Germany were the first two countries to quit the bidding race and were followed by Argentina. Two others, Turkey and United Arab Emirates, had also been interested but have since withdrawn.
FINA was forced to find a new host city for 2021 after the Mexican city of Guadalajara withdrew as the 2017 host, citing financial problems caused by falling oil prices.
Budapest, which had originally been awarded 2021, agreed to step in at short notice and host the biennial event in 2017 but a new site for 2021 was needed, with Gwangju, South Korea already confirmed for 2019.
China and Japan both put forward several candidate cities but have now finalised their preferred choices, Marculescu said.
Nanjing, the capital of Jiangsu province, was the host city for the 2014 Youth Olympics while Fukuoka was the site for the 2001 swimming world championships.
The tiny but ambitious Qatar has been steadily scooping up more and more of the world's major sporting events as other potential bidders drop out, often spooked by the enormous costs.
Oil and gas-rich Qatar has already been awarded next year's road cycling world championships, the 2018 gymnastics world championships, the 2019 athletics world championships and the 2022 Soccer World Cup.
(Editing by Amlan Chakraborty)
