Reports emerged on Friday suggesting Coutinho had handed in a transfer request, although they were denied by Liverpool.
The midfielder has been the subject of two bids from the Spanish giants – £70million and £90m – but both have been rejected
And in a statement, a family member has claimed Coutinho is annoyed with the club’s refusal to entertain a move away.
In a statement on Friday, the club’s owners Fenway Sports Group club said its “definitive stance” was that “no offers will be considered”.
It added: “Philippe will remain a member of Liverpool Football Club when the summer window closes.”
Coutinho, who scored 14 goals last season, signed a new five-year deal in January, which did not include a release clause. He joined Liverpool from Inter Milan for £8.5m in 2013.
Manager Jurgen Klopp said the Reds were not “a selling club” when Barca’s previous £72m offer was rejected in July.
Barcelona have also had a bid rejected for Borussia Dortmund’s 20-year-old forward Ousmane Dembele since they sold Brazil forward Neymar to Paris St-Germain for a world record £200m last week.
The German club confirmed they met Barca representatives but the offer did not meet their valuation of the France international.