The Premier League side, who currently sit ninth in the standings respectively ahead of their Sunday clash with Crystal Palace, are interested in recruiting the AC Milan left winger come the end of the current 2015-16 campaign.
The 26-year-old, who has two international caps for his country, has scored an impressive seven goals and provided nine assists in 30 appearances in all competitions for the Serie A outfit so far this season.
Bonaventura; who is also attracting Bundesliga club Wolfsburg this summer, is demanding a pay rise at the San Siro, which has put Jurgen Klopp’s Reds on high alert about his availability in the short-term future.
The report suggests that the Italian forward could be offloaded for around £14.2m.
Bonaventura has found the back of the net 14 times in 64 first-team games for Milan since arriving from Atalanta back in September 2014.