Barça were thwarted in their attempt to prise Coutinho away from Anfield during the summer with Liverpool placing a reported 200 million euros ($238 million) asking price on the midfielder.
Despite the player trying to engineer a move, Liverpool turned down his late transfer request during the close season window.
But Grau made clear the La Liga giants had not given up the chase.
"We are ready to sign Coutinho, or any other player (during the winter transfer window)," he said at a press conference on Wednesday.
"We have the money," Grau said, confirming the club's announcement in July of record income of 708 million euros ($812.8m) for 2016/2017 with an after-tax profit of 18m euros.
Grau added: "The most important thing is the demands from the management, and we will do everything possible to meet them. We want to have the most competitive team possible."
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Barça experienced a tumultuous time during the summer transfer market, losing Coutinho's compatriot Neymar to Paris Saint-Germain for a world record 222 million euros, and bringing in Ousmane Dembele from Borussia Dortmund for 105 million euros.
But Dembele has endured a nightmare start to life at the Camp Nou. The France international suffered a hamstring injury on his full La Liga debut ruling him out until January at the earliest.