Mr Trump claimed the FBI should be looking into his former opponent Hillary Clinton instead, tweeting: "I feel sure that we will soon be getting to the bottom of all of this corruption. At some point I may have to get involved!"
Critics interpreted it as another indication the president is considering intervening in the Russia investigation.
"This latest thread implies a willingness to obstruct justice," historian Timothy Naftali, clinical associate professor of public service at New York University, told CNN. "He is sending a signal he wants to stop this process."
Mr Trump also repeated his criticism of attorney general Jeff Sessions, who recused himself from the Russia investigation and has said he will not allow the Department of Justice to be influenced by political considerations.
"Jeff Sessions said he wouldn't allow politics to influence him only because he doesn’t understand what is happening underneath his command position," the president tweeted.
It follows speculation that the president could use his powers to pardon Mr Manafort and Mr Cohen.
The president has already pardoned the highly controversial former Arizona sheriff Joe Arpaio, who was convicted of contempt of court.
Last month Mr Trump claimed he also had the "absolute right" to pardon himself in relation to the Russia investigation, while insisting he had done nothing wrong
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