The 22-year-old has been in good form for his new side since making a £15 million summer switch from Swansea and is desperate to help his team record their first league win of the season on home turf against their rivals.
"Playing against United at Anfield is exactly the kind of reason I came to Liverpool,” Allen told the Liverpool Echo.
"There aren’t many games bigger in world football. I’m really looking forward to experiencing it for the first time.
"We’re all looking forward to playing at Anfield and what better game than to be playing United. I’m enjoying my football. I feel fantastic and the club has welcomed me and helped me settle.
"Life is amazing at the moment. Everything seems to have happened at once. It’s been a roller-coaster for me. All of my dreams are being fulfilled at the moment and long may that continue.
"The game coming up at the weekend will be another little landmark for me and we want the three points."
After being beaten by Arsenal at home before the international break, Liverpool bounced back to pick up a point at Sunderland last weekend and Allen believes the side are beginning to demonstrate the ethos that manager Brendan Rodgers is aiming for.
He added: "What we did against Sunderland, that’s the idea of how the manager wants us to play. The idea is to control football matches and Liverpool should be doing that.
"The ability and quality in the team suggest we should be able to. That’s the most positive and beneficial way of playing football and winning games.
"Sunderland was a good example of being courageous and controlling the match in terms of possession. It’s a sign of things to come.
"For me personally, Sunderland wasn’t as quite a high standard as I’d have liked, and hopefully I can put it right against United."