It's likely the Anfield club will be upset with Grau's comments having written to Barcelona urging them to stop trying to unsettle Coutinho.
Liverpool made their stance clear when they rejected Coutinho's transfer request and rebuffed Barcelona's bids of £72 million, £90.3m and £118m.
Liverpool forward Philippe Coutinho could reportedly complete a midseason move to Barcelona after being "promised" a January move to the Camp Nou following his failed attempt to secure a summer exit.
"Right now there is nothing planned for the January window. We want to have the most competitive team possible", Grau said. "We weren't going to give €200m or €150m - we chose to step away from such an expensive market, our offer was less than €100m, with add-ons it could have reached €120m".
Speaking to the Daily Telegraph, Carragher said: "It's a new position that he has been playing for Liverpool but he has been outstanding".
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.
That this comes in the buildup to another big game for the Reds, who take on Man United at Anfield on Saturday afternoon, continues a trend from Coutinho's suitors.
Furthermore, Barcelona are determined to advance his arrival to January in order to avoid Paris Saint-Germain joining the race next summer.