The Mexican international left United in the summer to join Bayer Leverkusen, for whom he has been prolific – scoring 22 goals in 26 games for the Bundesliga outfit.
Klopp’s interest in the 27-year-old was first noted by the Times back in January, and reports in Italy have now added to the speculation.
Bayern Munich – who next season will be managed by Hernandez’s former boss Carlo Ancelotti – are also mentioned as potential suitors.
The Reds have struggled up front this term, largely due to injuries to attacking players, and the goalscoring instincts of ‘Chicharito’ could help remedy that situation.
Forwards Daniel Sturridge and Divock Origi both returned from injury at West Ham United on Tuesday, but the former’s fitness problems over the last two years may see him move on, as the Telegraph claimed last week.