The Reds are said to have softened their stance regarding his departure and it is expected that they will sanction the transfer if the Catalan giants meet their valuation.
According to BBC Sport, Barcelona are preparing a fresh bid for the Reds midfielder, their first since their three failed attempts in the summer. The La Liga outfit's last bid was £118m ($159m, €132m), which was rejected by Liverpool, but they are set to return with an improved offer in order to complete the long-running transfer saga.
The report claims their last £118m bid included add-ons, but will have to return with an improved offer that is not loaded with add-on payments. According to Spanish publication Sport, the price is the only sticking point that is holding back the deal after numerous meetings between the player's agents and the Spanish club.
It is believed that Liverpool are unwilling to lower their €150m (£133m) valuation while Barcelona are not yet ready to go above €130m at the moment. The latter are keen for the move to go through in the coming week and hope that the difference can be settled through add-ons, but the bid will have to be better than the previous terms offered.
Coutinho is said to be keen to complete the move with reports suggesting that he has already agreed terms on a five-year deal. He is expected to sign a contract that will see him earn around £203,000-a-week.
Barcelona players Luis Suarez and Paulinho have already stated their desire to play with the Brazil international, while the club's kit manufacturers Nike jumped the gun after they invited fans to design their own Coutinho kit, stating that the Brazilian is 'ready to light up the Camp Nou'.
The 25-year-old Reds midfielder, who is currently sidelined with a minor injury, cannot play in the Champions League if he moves to Barcelona, but the La Liga outfit remain unconcerned about that fact as they look to complete the move as early as possible.