The Catalan giants reportedly had three bids - one in the region of £118m - rejected by the Premier League club during the summer transfer window.
"We are prepared to sign Coutinho or other players but the proposal has to come from the technical staff".
Liverpool are understood to be angered by Barcelona's latest attempt to unsettle their player and could do without the distraction in the week they lost Sadio Mane for six weeks to a hamstring injury on worldwide duty.
Nevertheless, the timing of Grau's comments will not please Jurgen Klopp as he looks for his players to refocus after the worldwide break with a huge match against Manchester United on the horizon on Saturday. "The club will remain sustainable, we don't want losses and we have to continue to look for ways to generate income".
But Grau suggested that some players would have to leave the Nou Camp to clear the decks for planned arrivals, despite the £198 million banked from Neymar's controversial defection to Paris Saint-Germain.
Coutinho had his heart set on moving to Barca and handed in a transfer request on August 11; Liverpool, however, insisted they would not give him his wish and warned Barcelona to stay away.
Liverpool were upset by Barca's very public pursuit of their star player in the summer and are less than impressed by yesterday's latest unwanted development.
Barcelona have turned up the heat on Liverpool and will bid £120million for Philippe Coutinho again in January.
According to El Mundo Deportivo, the attacking midfielder was promised he would be sold in January, although Barcelona still need to find an agreement with Liverpool.