The 21-year-old has previously worked with Reds boss Brendan Rodgers first at Chelsea and then when he went on loan to Swansea in the 2010/11 season.
Borini has now arrived at the club's Melwood training ground to have his medical, Press Association Sport understands, and the deal should be completed, barring any hitches, in the next couple of days.
Borini's fee has not been disclosed but it is not believed to be as high as the £12million being reported in some quarters.
Source: PA