The offer, made with Vladimir Putin's trademark sardonic humour, came as the Russian president poured scorn on Comey for his role in a row in Washington over alleged Russian meddling in last year's US presidential election.
At a congressional hearing this month, Comey said Trump asked him to drop an investigation into contacts between Trump associates and Russian officials, while the US president has accused Comey of not telling the truth.
Asked about Comey at a question-and-answer session with Russian voters, Putin said it was "strange" that, while still FBI director, Comey had passed the contents of a conversation he had with Trump to the media via a friend.
"What is the difference then between the FBI director and Mr. Snowden?" Putin said, referring to former US National Security Agency contractor Edward Snowden, who was granted asylum in Russia in 2013 after leaking classified information about US spy operations.
"In this case, he (Comey) is not the head of a special service but a human rights activist who defends a certain position," Putin said.
"By the way, if he is subject to any sort of persecution in connection with this, we will be ready to give him political asylum in Russia. And he should know about this."
"I am not familiar in detail with the testimony given by former FBI director Comey," Putin said. "Again, he gave no evidence of this (Russian interference)."
"And what about constant US propaganda, constant US support of America-oriented non-governmental organisations by giving them money directly? Isn't it an impact on our minds? Isn't it an attempt to influence how we should behave during election campaigns? This continues year after year," he said.
Putin said many heads of state around the world had told him of similar US meddling in their internal affairs. But they would not voice their concerns openly, fearing they would "spoil relations" with Washington, he said.
As for Russia, "we have an opinion of our own, we express it openly. But this is not any sort of underground, subversive activity", Putin said.
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