Coutinho is currently on loan at Bayern Munich from Barcelona, and the Bundesliga champions will have the chance to sign the Brazil international on a permanent deal at the end of the 2019-20 campaign.
Bayern are allegedly unlikely to take up the £102m option, though, which has led to claims that Barca could sell the attacker for £68m this summer.
Manchester United and Manchester City have both been linked with the 27-year-old, but according to The Express, Liverpool could attempt to re-sign him.
The report claims that Bayer Leverkusen's Kai Havertz is the Merseyside club's leading transfer target ahead of the summer transfer window, but Klopp would be interested in Coutinho if the European champions are unable to secure a deal for the Germany international.
Barca signed Coutinho from Liverpool in January 2018 in a deal that could eventually reach £142m, but the South American has largely struggled to make his mark at Camp Nou.