The 20-year-old signed for Parma at the end of last season, and was immediately loaned out to Serie A rivals Roma.
Borini failed to make the grade at Stamford Bridge, and spent part of 2010-11 on loan at Swansea before his Chelsea contract expired at the end of the campaign.
However the Italy U21 international has always been highly rated in England, and despite never making a Barclays Premier League appearance, Liverpool considered taking a gamble on Borini in the summer.
Reds boss Kenny Dalglish instead opted to complete a deadline-day move for former striker Craig Bellamy, who returned to Anfield on a free transfer from Manchester City.
"Parma did well to believe in him when his contract ran out at Chelsea," said Borini's agent Marco De Marchi.
"Then Roma invested heavily on him which confirmed that the player has some extraordinary ability, as you can see from his performances for the Italian Under-21 side.
"The player was liked by a lot of other clubs, sides such as Liverpool and Hamburg came after him too."