That's according to beIN Sports reporter Tancredi Palmeri.
The Italian says Barca have not given up on the forward despite having bids worth £72m and £91m rejected.
The rebuttals prompted Coutinho to email in a transfer request which was immediately rejected.
Liverpool insist Coutinho has no price and will not be leaving but the Catalan giants are not giving up easily.
Palmeri tweeted: "Barcelona have assured Coutinho they will up their bid to Liverpool and won't give up on negotiation.
"Coutinho being pessimistic."
Coutinho handed in his request on Friday just hours after Kop owners FSG released a statement saying he would be staying.
The Brazilian has been missing from action recently with a bad back.
He has not been named in the squad to face Hoffenheim in their Champion League qualifier tomorrow night.
