Mr Trump also told NBC News it was his decision alone to sack James Comey.
Mr Comey was leading an inquiry into alleged Russian meddling in the US election and possible collusion between Trump campaign officials and Moscow.
Mr Trump has dismissed the probe as a "charade", a claim directly contradicted by Mr Comey's successor.
In his first interview since firing the FBI director, Mr Trump told NBC News on Thursday he had asked Mr Comey whether he was under investigation.
"I said, if it's possible would you let me know, 'Am I under investigation?' He said: 'You are not under investigation.'"
Media captionWhat do Trump supporters think about Comey's firing?
"I know I'm not under investigation," Mr Trump told the interviewer, repeating a claim he made in Tuesday's letter of dismissal to Mr Comey.
The president also appeared to undercut the initial White House explanation that he fired Mr Comey on the recommendation of top justice officials.
"He's a showboat. He's a grandstander. The FBI has been in turmoil. I was going to fire Comey. My decision," Mr Trump said.
"I was going to fire regardless of recommendation."
"There's no collusion between me and my campaign and the Russians," he added.
Mr Trump recently tweeted that the Russia-Trump collusion allegations were a "total hoax".
But on Thursday he denied he wanted the FBI inquiry dropped.
"In fact, I want the investigation speeded up," the president told NBC.
Mr Trump said he had just sent a letter via a law firm to Republican Senator Lindsey Graham stating that he has no stake in Russia.
"I have nothing to do with Russia," he said. "I have no investments in Russia. I don't have property in Russia. I'm not involved with Russia."
On Thursday afternoon Mr Trump retweeted a five-month-old post by comedienne Rosie O'Donnell, his arch-foe in the world of entertainment.
Many liberals had previously called for Mr Comey to be removed, blaming his updates last year about the FBI inquiry into Hillary Clinton's emails for Mr Trump's shock election victory.
The White House has depicted the Russia inquiry as "probably one of the smallest things" that the FBI has "got going on their plate".
But acting FBI Director Andrew McCabe said on Thursday that it was "a highly significant investigation".
In testimony to the Senate Intelligence Committee, he also cast doubt on White House claims that Mr Comey had lost the confidence of his staff.
"I can confidently tell you that the vast majority of employees enjoyed a deep and positive connection to Director Comey," Mr McCabe said.
The acting FBI director vowed not to update the White House on the status of the investigation and to notify the Senate panel of any attempt to interfere with the inquiry.
Republican committee chairman Richard Burr asked Mr McCabe if he had ever heard Mr Comey tell Mr Trump the president was not the subject of investigation.
Mr McCabe said he could not comment on an ongoing inquiry.
The acting FBI director did not confirm reports that Mr Comey had asked for more resources for the agency's Russia inquiry.
Mr McCabe said he believed the FBI had sufficient funding to conduct the probe.
Rosenstein's way out - Anthony Zurcher, BBC News, Washington
Deputy Attorney General Rod Rosenstein - who penned a memo detailing Mr Comey's "serious mistakes" - brought a reputation for even-handedness and probity with him to the job of deputy attorney general. Two weeks later, that reputation is being put to the test.
Such is life in the Trump White House, where every appointee and aide is just one tweet, event or press conference away from the maelstrom.
On Tuesday night, as the administration press shop scrambled to explain the president's surprise decision to sack his FBI director, Trump supporters leaned hard on Mr Rosenstein's credentials to paint the move as a nonpartisan decision based on Mr Comey's overall job performance.
The deputy attorney general reportedly balked at the characterisation that he was the driving force behind Mr Comey's dismissal, however.
Mr Rosenstein's threat to resign is different than actually packing bags, of course, and his fate at this point is still tethered firmly to the president he chose to serve.
There is a way out, though. Due to Attorney General Jeff Sessions' recusal on the matter, it's Mr Rosenstein's call whether to appoint a special counsel to head the Justice Department's Russia investigation. It may be the one card he can play to sidestep the growing frenzy that spins around him.
At the centre of the storm - Rod Rosenstein
- 52-year-old Harvard graduate confirmed by US Senate as Deputy Attorney General on 25 April
- Had strong bipartisan backing with 94-6 vote in his favour
- Overseeing federal investigation of alleged Russian interference in November's elections, after Attorney General Jeff Sessions, recused himself over meetings with Moscow's envoy in Washington
- Appointed by President George W Bush as US attorney in Maryland and kept on by President Barack Obama
- Reputation as apolitical and professional
- Wrote memo detailing "serious mistakes" by Mr Comey, but did not expressly call for his removal