The 23-year-old Italian has made just three appearances for the Reds this season after turning down moves to Sunderland and Queens Park Rangers in the summer.
While admitting that it has been difficult for him to adjust to a lack of first-team action at Anfield, Borini remains hopeful that he can make a positive impact on Brendan Rodgers's side.
"It was difficult mentally to deal with the situation from one day to another but in my head it was clear that I wanted to stay here and fight for my place," he told Sky Sports News.
"That's what I have always said in the past and what I have always wanted to do and I am showing it every day in training."
Liverpool continue their Premier League campaign on Sunday when they face QPR at Loftus Road.