The Brazil international signed a four-year contract at Anfield in May after a fee of close to £44m was agreed between the two clubs.
Liverpool appeared to snare Fabinho before Premier League rivals United could get a deal over the line, with the Red Devils repeatedly linked over the past couple of windows.
Despite conversations with United previously taking place, the 24-year-old insists that Merseyside was always his favoured destination once Liverpool stepped forward with an offer.
"I was never close to signing for Manchester United, no," he told FourFourTwo. "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. 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."
Fabinho made 225 appearances for Monaco over a five-year stay, scoring 29 goals from a deep starting position in midfield.