Mr Mueller is said to be examining the letter as part of a wide-ranging investigation into the alleged Russian interference in the presidential campaign last year.
The investigation includes looking into whether or not President Trump obstructed justice by firing Mr Comey, who was previously in charge of investigating the Republican President.
After sacking Mr Comey President Trump reportedly had a letter delivered to the former FBI boss which explained the decision.
The letter, written by deputy attorney general Rod Rosenstein, focused on Mr Comey’s handling of Hillary Clinton’s use of a private email server.
However, Mr Mueller is allegedly in possession of an earlier letter justifying the firing that was blocked by the White House.
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Mr Trump was talked out of sending the earlier letter to Mr Comey by White House lawyer Don McGahn, according to the New York Times.
The newspaper, which explained that it had not seen the actual letter, reported that Mr McGahn “believed that some of its contents were problematic”.
President Trump reportedly wrote the letter with the help of his White House aide Stephen Miller.
The earlier letter could provide Mr Mueller with evidence of Mr Trump’s true intention for dismissing his FBI Director, it has been suggested.
But it is unknown how much of the rationale in the original letter focused on the Russia investigation.
Shortly after firing Mr Comey in May, President Trump admitted in an interview with NBC that the Russia probe had been on his mind when he made the decision to fire the FBI director.
In the interview, he said: “Regardless of recommendation, I was going to fire Comey.”
He added: “And in fact, when I decided to just do it, I said to myself, ‘You know, this Russia thing with Trump and Russia is a made up story.”