The 21-year-old joined his former Swansea City boss, Brendan Rodgers, at Anfield for a fee believed to be around £10.5 million earlier in July after notching 10 goals in 26 appearances for Roma.
"I hope to bring goals to Liverpool. I want to bring goals and add value to the team. I want to be a big player here," Borini told the Daily Mirror.
"In Italy I think I did well with Roma, but it is a little bit different being there as a young player because you're not seen as a big star. You always have to do the hardest thing to get noticed.
|2/1||Liverpool are 2/1 with William Hill to finish between second and fourth in the 2012-13 Premier League
"I was the youngest player in the team at Roma, it was just thanks to Luis Enrique that he gave me the chance to play.
"But I want to be a focal point of the team at some stage of my career. Maybe it could be now. I don't want to move every season, I want to stay in this team for many years, and be an important part of the team.
"I don't know if it is a good thing or a bad thing, but I have always wanted everything the quickest way possible - I have the ambition to get there quickly."
Borini became a fans' favourite at Roma last season and he is hoping that his famous 'assassin' celebration proves a hit with the Kop in the upcoming campaign.
"The celebration is something I did with my friends when I was in the youth team at Chelsea," he revealed.
"In Italy, we say when one person wants something so much it is like he has a knife between his teeth - like a warrior who never gives up.
"After that, I kept doing it. I did it the first time I scored at Swansea and everyone liked it. It was the same at Roma."