The officer said Andrew may have returned to Buckingham Palace in the early hours of March 11, when he said he was at home after taking his daughter to Woking's Pizza Express.
In an interview with the Mail on Sunday, the officer recalled the Prince arriving by car at the Palace and claimed he shouted at guards when the gates weren't opened quickly enough.
He told the newspaper he believes it could have been the same evening the Duke is accused of having sex with Ms Giuffre, then Virginia Roberts, at the home of socialist Ghislaine Maxwell.
Ms Giuffre, who was 17 at the time, alleges she was coerced into having sex with Andrew after being flown to London by serial paedophile Jeffrey Epstein, who died last year.
Andrew categorically denies he had any form of sexual contact or relationship with Ms Giuffre, and told Emily Maitlis on BBC's Newsnight that it "couldn't have happened" because he was at home the night in question.
He said: "I was at home, I was with the children and I'd taken Beatrice to a Pizza Express in Woking for a party at I suppose four or five in the afternoon.
"And then because the Duchess was away, we have a simple rule in the family that when one is away the other one is there."
It was assumed that when Andrew said he was at home, he meant Sunninghill Park, in Berkshire, which he shared with his ex-wife Sarah Ferguson and their daughters.
It is around 10 miles from Woking, in Surrey.
But speaking to the Mail on Sunday, the officer said the night he recalled Andrew shouting at Buckingham Palace guards could be the same night he is accused of having sex with Ms Giuffre.
The officer, who spoke to the newspaper on the condition of anonymity, had an "exemplary" 23-year career with Metropolitan Police and refused payment for the interview, saying that he just wanted to "see justice done", the newspaper said.
He said he wants to access his shift roster and other documents to make sure his account is accurate and is planning on using data protection and freedom of information laws to obtain them from Metropolitan Police.
He said: "Having considered Prince Andrew's alibi with my own recollections, it is my belief that the abusive confrontation with the royal could have been in the early hours of Sunday March 11, 2001.
"To be 100 per cent certain I would like access to my duty roster for that month. I believe I have a right to know my own shift patterns."
He added: "After seeing the BBC interview, it dawned on me that the abusive incident I experienced could cast doubt on Prince Andrew's alibi if it were the same night."
A spokeswoman for Metropolitan Police told the Standard the former officer is "entitled to submit his subject access request which will then be considered".
She added: "We are not prepared to discuss records that we may or may not hold regarding matters of protection. We are not conducting a criminal investigation."
Andrew categorically denies he had any form of sexual contact or relationship with Ms Giuffre.
Buckingham Palace previously branded the allegations “false and without any foundation”, stating: “Any suggestion of impropriety with underage minors” by the duke was “categorically untrue”.
The Palace said it is not commenting on the ex-officer's claims.