The 21-year-old striker is set to complete the switch in a few days as the offer will help Roma raise nearly £6 million in profits on the young striker.
Borini joined the Chelsea youth academy as a 16-year-old under Rodgers who later took him on loan to Swansea, where the youngster played an important role to help the Welsh club get promoted to the Premier League.
The prolific young Italian striker was also included in Cesare Prandelli's Italy squad at the Euro 2012 tournament after a successful campaign with Roma in his first spell in Serie A.
As a 16-year old Chelsea player, Borini was regarded as a promising young talent but he joined Parma and was quickly loaned out to Roma who immediately took over 50 per cent possession of the striker after impressing at the start of the season.
However, Roma bought the player in a deal worth £6 million from Parma to avoid complications of joint ownership.
Meanwhile, Liverpool have agreed to double that fee to land the young Italian striker which could see Anfield's £35 million forward Andy Carroll move away on loan after interests from several clubs like West Ham United, Newcastle United, Fulham and even AC Milan.
Borini is known for his tactics and speed in front of goal. He is comfortable to play on either right, left or as a main forward. He has the ability and desire to be the first to receive the ball and even assist to regain possession.