The 25-year-old has been heavily linked with a move to Camp Nou after Barcelona lost Neymar to Paris Saint-Germain, but Liverpool have so far remained steadfast in their refusal to sell their star asset.
However, Liverpool owners Fenway Sports Group reportedly told Coutinho before the international break that he would be granted his request to leave before Thursday's transfer deadline.
The deal would make Coutinho the second most expensive player of all time behind only compatriot Neymar, setting a British and Spanish transfer record in the process.
Coutinho has missed Liverpool's opening three games of the season due to a sore back and illness, although he was described as being in "perfect condition" to play for Brazil during the international break.
Coutinho has scored 42 goals in 182 appearances since joining Liverpool in 2013, including a career-best 13 in the Premier League last season.