The England international said this ahead of Liverpool’s away Premier League clash with Tottenham Hotspur on Sunday.
Liverpool and Man United are the most successful clubs in England.
The two Premier League top clubs have been fighting for bragging rights for decades and the rivalry between them runs deep.
Asked whether he would retire or play for Man United, Alexander-Arnold told Sky Sports: “Right now, [I would] retire, to be honest, could not do that [join Manchester United].”
Alexander-Arnold also revealed that he prefers playing against Man United than featuring in the Merseyside derby against Everton.
The 23-year-old said: “I mean, Manchester United is a bigger game historically. I’d say Manchester United, more people watch it.”
Alexander-Arnold helped Liverpool to a thumping 5-0 win over Man United in October.
Liverpool currently sits in the second position on the log with 13 points ahead of Man United, though the Red Devils have a game in hand.