Coutinho had already moved to Europe prior to his Liverpool switch, turning out 47 times for Inter Milan, but the Reds may be wise to make a swift move for his young countryman before someone beats them to the punch.
News of a winter move would be odd considering Barcelona would still need to beat the offers said to have been made in the summer.
"We are ready to sign Coutinho or any other player the technical staff request in the winter window", Grau said.
From Barcelona's point of view, the Brazilian will be cup-tied in the Champions League, which means there will be little value in signing a player they can not feature in their most important competition.
Yet despite Grau's comments, Spanish football expert Guillem Balague remains doubtful that Barça will actually submit a bid for the Brazilian in January.
"Of course they are still interested in Coutinho, they've got everything sorted with the player, we've all known that for months".
He stated: "The sale of Neymar allowed us to get into the market and take some players we wanted".
At this stage of the season, the hope will be that Coutinho ignores Barcelona's advances and continues to focus on his form at Anfield. The midfielder missed Liverpool's opening matches of the new season due to a reported back injury, only to score for Brazil when he joined up with the Selecao for worldwide duty.
Coutinho has since found the back of the net in his next two games against Russian side Spartak Moscow and promoted side Newcastle United.
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