"I hope you can let this go," Mr Trump reportedly told Mr Comey after a White House meeting in February, according to a memo written by the ex-FBI director.
The memo was written immediately after the meeting, a day after Michael Flynn resigned, according to media reports.
The White House has denied the allegation in a statement.
Media captionA wild week for Trump in Washington
"The president has never asked Mr Comey or anyone else to end any investigation, including any investigation involving General Flynn," it said.
Mr Flynn was forced out in February after he misled the vice-president about his conversations with Russia's ambassador before Mr Trump took office.
The latest Russian twist, first reported by the New York Times, comes a week after Mr Trump fired Mr Comey over his handling of the FBI investigation into Hillary Clinton's use of a private email server while at the state department.
Mr Comey's dismissal sent shockwaves through Washington, with critics accusing the president of trying to thwart the FBI investigation into Russia's alleged interference in the US election and any Moscow ties to Trump associates.
Mr Comey reportedly wrote a memo following a meeting with the president on 14 February that revealed Mr Trump had asked him to close an investigation into Mr Flynn's actions.
He reportedly shared the memo with top FBI associates.
"I hope you can see your way clear to letting this go, to letting Flynn go," the president told Mr Comey, according to the memo. "He is a good guy."
Mr Comey did not respond to his request, according to the memo, but replied: "I agree he is a good guy."
In response to the report, a White House official pointed out that acting FBI director Andrew McCabe had testified last week that there had been "no effort to impede our investigation to date". READ MORE
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