Reports in British media put the latest bid at 125 million euros ($146.85 million), as the Spanish club continue to seek a replacement for Coutinho's Brazil team mate Neymar, who they sold to Paris St Germain for a world record 222 million euros earlier this month.
Manager Juergen Klopp has previously insisted that the 25-year-old would not be sold, although last weekend he said that if Liverpool's owners decided to accept a bid there was nothing he could do about it.
Coutinho will miss Saturday's match at home to Crystal Palace because he still has a back injury, Klopp told reporters on Thursday.
(Reporting by Steve Tongue; Editing by Christian Radnedge)
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