According to Football Italia, the Reds are keen to bring 20-year old Spanish-born Senegalese forward Keita to Anfield in exchange for Borini.
Former Chelsea and Swansea City attacker Borini has failed to impress for the Reds since arriving from Parma in 2012 and is expected to be offloaded this summer.
Regarding a potential move for Keita, his agent Ulisse Savini said: "Liverpool have a manager who relishes attacking players like Keita.
"It is a destination we would like, but we have to verify a series of situations. So far I have not had any direct contact with Liverpool."
Furthermore, Gazzetta dello Sport suggests that Lazio have agreed terms with Borini for an initial season-long loan with a view to a permanent move but there was no talk of a swap involving Keita.