Barca are in the market for a new centre-back in the January transfer window following recent injuries to Samuel Umtiti and Thomas Vermaelen and apparently Lovren is on their shortlist.
The Croatia international only made his first Premier League start of the season before the international break against Manchester City as he's had to bide his time since recovering from an abdominal injury with Joe Gomez and Virgil van Dijk Reds boss Jurgen Klopp's preferred first-choice partnership so far this season.
A move to the Nou Camp for the former Southampton man would come as a surprise but Barca may have been alerted to the 29-year-old following some impressive displays in the second half of last season and during the summer at the World Cup when he helped his country to the final.
Meanwhile, reports say Brazilian star Firmino is also wanted by Barca, who are beginning the search for a long-term replacement for former Liverpool forward Luis Suarez.
The Uruguay star is now 31 and there are concerns he may not be able to maintain his goalscoring form for much longer in La Liga whereas Firmino, who is 27, is just coming into his peak years.
It is claimed ex-Reds playmaker Philippe Coutinho has recommended Firmino to the powers that be at Barca and the club are mulling over making a big-money bid in excess of £80million for him next summer.