The Catalan club believe that the Merseyside club will find it hard to turn down a bid in the region of £89 million.
La Blaugrana's new boss Ernesto Valverde is clearly an admirer of the 25-year-old and he has been linked, nearly incessantly this month, with a switch to the Camp Nou.
He tweeted: "Here we go: Barcelona have bid €70m for Coutinho".
Signed for £8.5m from Internazionale in 2013, Coutinho has slowly worked himself into a position of being a pivotal member of the Liverpool line-up.
Liverpool have declared the player is not for sale, but there is a suggestion that, secretly, they would consider an offer of €100m.
Barcelona believe if they can bring Coutinho, it might make Neymar more happy and comfortable, leading to him staying.
And Murphy believes Coutinho leaving would not necessarily weaken Jurgen Klopp's side, particularly if they invested the money wisely.
The Argentinian scored eight goals and managed two assists in the Premier League last season, and he is under contract until 2020 at the London Stadium.
The paper claims that despite Liverpool's insistence the player is not on the market they "will sell if the clubs agree on a good transfer figure".
Liverpool can only hope that Coutinho does not have his head turned by the Spanish giants, although that is easier said than done.
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