Liverpool rejected three bids from Barca during the summer - the last of which was in the region of £118 million.
But Grau made clear the Spanish giants had not given up the chase.
"We are [financially] prepared to sign Coutinho or any other player in January".
At the start of the summer, he was being linked with a move to Barcelona on the recommendation of his Brazilian team mate, Neymar. We are putting all the resources of the club [to improve the squad]. If this is the case [If Barcelona sign players in January] we have to generate income and maybe someone have to leave.
However, there is no indication of what such a bid would be although the report does suggests it would be similar to those lodged during summer, thought to be €110m, of which €80m was paid up front.
Liverpool will hope the latest news out of Spain will not disturb him ahead of their crunch clash with Manchester United at Anfield on Saturday or months of fresh speculation.
After missing the first seven games of Liverpool's campaign, the attacking midfielder has scored in their last three matches.