The Catalan giants reportedly had three bids - one in the region of £118m - rejected by the Premier League club during the summer transfer window.
The Reds managed to keep hold of the Brazilian, who was understood to have been keen on moving to Camp Nou, despite committing to a new long-term contract at Anfield in January.
A report in the Spanish press has claimed that Liverpool have agreed to sell their playmaker in January if Barca return with an acceptable offer.
"We are ready to buy Coutinho in the winter market or any player the technical staff request," the Liverpool Echo quotes Grau as saying. "But it is important to adjust ourselves, so if there are to be arrivals, there must be exits as well.
"We must forget about the price paid for Neymar last summer. After taxes we received about €188m (£168m) in income and a direct financial impact on the club's treasury of €144m (£129m)."
Coutinho has scored in his last three successive matches for Liverpool.