It is the rekindling of the pursuit of Coutinho, though, that worries Liverpool supporters, who have already been dealt a huge blow this week with Sadio Mane being ruled out for 10 games with a hamstring tear.
Barca 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.
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.
Klopp failed to sign top target Virgil van Dijk from Southampton in the summer transfer window to leave the Liverpool boss with centre-halves Dejan Lovren, Joel Matip and Ragnar Klavan.
"We are [financially] prepared to sign Coutinho or any other player in January".
Grau announced Barcelona's income to have reached €708m (A$1,077m) for the 2016-17 season, with a record budget of €897m (A$1,201m) in place for 2017-18.
But he admits there must be departures to balance out any arrivals in the new year. The club will be sustainable, we don't want losses. We could [sign in January]. "We will see it".