The 23-year-old striker has impressed for Vincenzo Montella's side this term, netting five goals in 18 league appearances for La Viola despite regularly being used as back-up to first-choice forward Nikola Kalinic.
The Senegalese star has helped the Serie A outfit close in on a Europa League spot for next season, with the side currently sitting in fifth spot - seven points clear of nearest challengers Milan.
Liverpool head coach Jurgen Klopp is expected to make a move for a new attacker in the upcoming transfer window following a disappointing debut campaign for £32 million signing Christian Benteke, combined with the poor fitness levels of Divock Origi and Daniel Sturridge.
Former Aston Villa frontman Benteke has struggled to replicate his goal scoring form on Merseyside, with the 25-year-old scoring just eight goals in 34 appearances in all competitions this term.
According to the Metro, Babacar previously turned down a move to fierce Premier League rivals Manchester United earlier in his career, before joining his current side for a paltry £35,000. Liverpool are now expected to offer the Italian side around £4.7 million for his services.