Coutinho handed in a transfer request in an effort to engineer a move to the Catalan giants, who had three bids rejected as the Reds made clear they were ultimately unwilling to part with their star man.
The 25-year-old has since been eased back into the first-team picture, after a back injury, and has underlined his importance to Liverpool with goals in each of his past three outings.
Barca are unwilling to concede defeat in their pursuit of the Brazil midfielder and are set to test Liverpool's resolve in January - although any new arrivals must be offset by departures.
"We are ready to buy Coutinho in the winter market or any player the technical staff request," Barcelona chief executive Oscar Grau said.
"But it is important to adjust ourselves, so if there are to be arrivals, there must be exits as well."
Barca sold Coutinho's Brazil teammate Neymar to Paris Saint-Germain for a world record €222 million ($A332 million) fee in August.
But Grau said: "We must forget about the price paid for Neymar last summer. After taxes we received about 188 million euros in income and a direct financial impact on the club's treasury of 144 million euros."