Borini was the subject of bids from Sunderland and QPR in the transfer window, both of which were accepted by Liverpool.
The Italian, though, surprisingly turned down both offers after manager Brendan Rodgers had reportedly informed the 23-year-old that he would receive limited first-team opportunities this season.
And, although he will face tough competition from the likes of Daniel Sturridge, Raheem Sterling and Mario Balotelli for a place in the starting XI, Borini is eager to prove himself to Rodgers.
"The transfer market was like a storm," Borini said in an interview with gianlucadimarzio.com.
"Now it has passed, I don't have problems anymore.
"I'm included in the Champions League's list, and we are training well. In the summer, there was a lot of talk, but there weren't big misunderstandings.
"My wish is to play in a top club and Liverpool is a top club. There have never been real problems, I know what my goals are and how I can reach them. Staying at Liverpool was one of them. I'm in a great team that tries to win every competition and that's what I want.
"If I stayed here, it's because I thought I can play. It's not out of thirst of greatness or to keep my spot here. I'm not like that. If I stayed at Liverpool it's because I think I could compete.
"Of course, there are excellent players here, but you can't win all the competitions with weak ones. I want to turn the great competition into an advantage and improve day after day."
