Reports linking the Italy international with the Anfield club earlier this summer came to nothing but it is understood that the Reds have now declared their interest in the former Manchester City star.
Any deal for the 24-year-old would be a permanent transfer, with a loan arrangement thought to be off the table.
Balotelli enjoyed a whirlwind stint at City between 2010 and 2013, winning an FA Cup and Premier League title with the club but gaining notoriety for his unpredictable off-field behaviour.
His tendency to appear in the gossip pages led to a famous goal celebration when, after scoring against neighbours Manchester United in October 2011, he lifted his shirt to reveal a slogan that read "Why Always Me?".
Balotelli eventually left England for Milan when then City boss Roberto Mancini decided to cash in on the eccentric forward.
Liverpool boss Brendan Rodgers has experience with difficult characters, of course, having coaxed the best out of Luis Suarez before his departure for Barcelona.
Suarez's disciplinary problems - including biting Chelsea's Branislav Ivanovic on Rodgers' watch - as well as a publicly stated desire to leave in 2013 caused headaches for Rodgers but the Uruguayan thrived on the pitch.
He swept the board at the end of season awards and the £65-75million Liverpool eventually banked from Barca largely funded a squad-building spending spree this summer.
But Rodgers remains in the marker for a marquee striker to share the load with Daniel Sturridge, with Rickie Lambert currently the only frontline support.
Monaco's Radamel Falcao is another big name who has been linked but Balotelli, who has been valued at around £17.5million, would be a more attainable target.
He scored 16 times for Milan last season, as well as grabbing Italy's winner in the World Cup opener against England in Manaus.
Milan club administrator Adriano Galliani said on Wednesday they had yet to receive an offer from the Reds for Balotelli, but on Thursday the Italian club's TV channel reported that the Rossoneri were in negotiations with the Premier League outfit over the striker.
Milan president Silvio Berlusconi, meanwhile, said previously he came close to selling Balotelli - who is under contract at the San Siro until June 2017 - to an unnamed English club before the World Cup.