The Reds have twice lifted the European Cup in the Italian capital, which hosts the Champions League final in May.
And Kop star Carragher wants to make it an incredible hat-trick by winning this season's competition.
He said: "The club has great memories of Rome.
"Obviously that's where it all started for us in the European Cup in 1977 and we then beat Roma on penalties in the final of the 1984 competition.
"That was a great achievement, so hopefully we can continue our history with Rome. It would be great to win another European Cup."
Liverpool start their Champions League campaign away to Marseille tonight.
He added: "I just think that all the best players in the world are in this country.
"That just shows the quality of talent in the Premier League."