Fina has urged whistleblowers to come forward after senior Russian anti-doping officials were accused of offering to stop testing the country's swimmers in exchange for money.
Reports claim former anti-doping chief Nikita Kamaev and Moscow laboratory director Grigory Rodchenkov asked for three million roubles (£32,200) a year.
The alleged offer, in 2011, was turned down by Russia's swimming federation.
Swimming's governing body described the claims as "very serious".
A statement read: "We urge anyone with relevant evidence to bring it forward to Fina so that we can share it with all appropriate authorities and take immediate disciplinary action if required."
The World Anti-Doping Agency (Wada) said its investigations team would also be examining the allegations.
According to reports in The Times and Germany's Frankfurter Allgemeine Zeitung, Kamaev and Rodchenkov offered to remove "two or three leading swimmers" from the testing group.
Russia was suspended from all track and field competition by the International Association of Athletics Federations in November after an independent report from Wada depicted a culture of widespread state-sponsored cheating by Russia's athletes, with even the secret services involved.
Rodchenkov, who is claimed to have been part of a state-sponsored doping conspiracy at the 2014 Winter Olympics in Sochi, is currently co-operating with a Wada investigation, while Kamaev died suddenly in February, aged 52.