Striker Borini spent the last campaign on loan at Sunderland, scoring 10 goals, and was widely expected to leave Anfield in the close-season.
However, the Italian turned down the chance to join Sunderland on a permanent basis, while also reportedly rejecting an approach from QPR.
The 23-year-old has made only three appearances so far this season after stating his wish to fight for a starting berth at Liverpool, but retains a belief that he can impress and enhance his international prospects with Italy.
Describing his goals for the season to the club's official website, Borini said: "Step by step, to get into the team as soon as possible and as much as possible.
"After that, I want to stay in the team, score goals and break my scoring record in the Premier League, and perform. I haven't changed my personality, but I have improved my game.
"I can offer hard work in performances every week and goals, as I did in the past. For Sunderland, I did very well and scored important goals.
"I can do the same here; with better players around me, it could probably be easier and with better results. I want to get back in the national team as well because that's a big aim.
"With a new manager [Antonio Conte], a new system and a new structure to the Italian national team, that can be a really good target for me, to get into the team and stay there as long as possible."
