The Premier League side, who currently sit second in the English top-flight standings after their opening 20 league games, five points adrift of league leaders Chelsea, is said to be interesting the La Liga giants after his impressive form during the start of the 2016-17 campaign.
The 24-year-old, who has 23 international caps for Brazil, has scored six goals and provided six assists in 14 appearances in all competitions for the Reds so far this season.
Coutinho, who has been ruled out of action since suffering ankle ligament damage against Sunderland on November 26, could return for Liverpool on Wednesday night in their EFL Cup semi-final first leg tie at Southampton.
However, manager Jurgen Klopp has warned Barca off any potential move for the Brazilian, saying, “We never had any ideas or plans or any talks about him leaving, because he is our player – there are no other ideas, nothing has changed.
“He is our player and that is it.”
The report quoted Barcelona are keen on a £60m deal for the Liverpool ace.