The 21-year-old Italian, signed in the summer from Roma, so far has only one goal to his name from 10 appearances across all competitions for the Reds - the opener in a 3-0 Europa League qualifying victory at home against Belarusian outfit FC Gomel.
He will be looking to boost his tally when Liverpool, now on their second match in Group A, welcome opponents from his native country to Anfield in the form of Udinese.
And Borini is confident it will not be long before he is properly into his goalscoring stride.
Reflecting on the strike against Gomel, Borini said: "It meant a lot because it was my first game at Anfield, so that was really nice.
"With the (first) Premier League goal, it is just a matter of time. As a striker, if you get into the right positions and you keep getting there, they (goals) will come."
He added: "At Liverpool the expectations are always high because it is a top club and it has to be this way.
"If I have come here, it is because I also have big expectations - that is why I chose this club."
Liverpool boss Brendan Rodgers is convinced Borini will be a success for the Reds.
"He is a young player I know very well and over time he will only get better and better," Rodgers said.
"He is a good kid who wants to work and there is no doubt over the coming years he will prove to be a very good player for the club."
While Borini has struggled to make an impact, a clutch of youngsters have certainly caught the eye in a Liverpool shirt this season, with 17-year-old winger Raheem Sterling, 18-year-old forward Suso and 19-year-old defender Andre Wisdom chief among them.
There has been talk of the trio being rewarded with new contracts and asked about the matter, Rodgers said: "I always believe you have to earn it, but there is no doubt that these boys have done well.
"It is something that we will look at over the next few months. There have been discussions between the club and representatives, but it is at an early stage."
Sterling received his maiden England Under-21 call-up yesterday [Wednesday], although Rodgers feels the teenager's current form would fully justify a recall to the senior international squad, which he was a part of for the first time last month.
Rodgers said: "In terms of whether he deserves a place (in the senior England squad), then of course - in terms of his performance level, he has been outstanding."