Fabinho was heavily tipped for a Premier League switch last summer following Monaco's impressive campaign both domestically and in Europe, but instead decided to stay at the Stade Louis II.
However, the 24-year-old insists that there was never an offer from United and also revealed that he did not have to think twice about joining Liverpool this summer.
"Yes, [it was] very easy. I was sad to leave Monaco, a club that gave me a lot of great moments, but in football sometimes you need new challenges and I thought it was time to move on," Fabinho told FourFourTwo.
"As soon as Liverpool declared their interest in signing me, it was a simple decision to make. A club with Liverpool's history wants you? Come on, you just pack your bags and go. It will be an honour to wear the famous red shirt.
"I was never close to signing for Manchester United, no. I heard things said about it, but the truth is it was never a strong possibility. I won't deny there were a few conversations about my situation with Monaco, but there was never an official offer from United."
Fabinho's first competitive appearance for Liverpool could come when they host West Ham United on the opening day of the season on August 12.