Russian Opposition politician Alexei Navalny was close to being freed in a prisoner swap at the time of his death, but President Vladimir Putin could not tolerate the thought of him being released and had him killed, a close ally said on Monday.

Navalny, 47, died at an Arctic penal colony on February 16. The Kremlin, which casts Navalny and his supporters as US-backed extremists, has denied state involvement in his death. Navalny's death certificate said he died of natural causes, according to supporters.

There was no immediate comment from the Kremlin and Navalny ally Maria Pevchikh, who is based outside Russia, did not present documentary evidence for her assertion.

Speaking on YouTube, Pevchikh said talks about exchanging Navalny and two unnamed US nationals for Vadim Krasikov, a Russian FSB security service hitman in jail in Germany, were in their final stages at the time of his death.

"Alexei Navalny could be sitting in this seat right now, right today. That's not a figure of speech, it could and should have happened," said Pevchikh, who chairs the board of Navalny's anti-corruption foundation.

"Navalny should have been out in the next few days because we got a decision about his exchange. In early February, Putin was offered to exchange the killer, FSB officer Vadim Krasikov, who's serving time for a murder in Berlin, for two American citizens and Alexei Navalny."

Krasikov was jailed for life in Germany after being convicted of killing an exiled Chechen-Georgian dissident in Berlin in 2019. Putin signalled in an interview with US journalist Tucker Carlson this month that he wanted to get Krasikov, whom he cast as a patriot, back.

A German government spokesperson declined to comment on Monday.

Pevchikh, who has been designated a "foreign agent" by Russia where the authorities accuse her of involvement in an extremist organisation, said she had received confirmation that negotiations for the swap were in their final stages on the evening of February 15.

Navalny, she alleged, had been killed a day later because Putin could not tolerate the thought of him being free. She did not explain why Putin had not simply refused to swap Navalny if he was opposed to such an exchange.

She said that businessman Roman Abramovich had been the one to float the idea to Putin of exchanging Navalny. There was no immediate comment from Abramovich.

Pevchikh did not name the two US nationals purportedly in contention to be swapped along with Navalny. But the US has said it is trying to return Evan Gershkovich, a reporter for the Wall Street Journal and Paul Whelan, a former US marine.