Danny Gallagher of MailOnline cited a report from Catalan daily Mundo Deportivo, which said the Brazilian had a verbal agreement with his employers and agreed to stay on at Anfield "providing he could move on in January."
Coutinho handed in a transfer request over the summer that was rejected, and Barca engaged in a public approach for the player, bidding three times and seeing each one of their offers turned down by the Merseysiders.
The most lucrative of those offers was worth in excess of £110 million, and despite being knocked back, Mundo Deportivo insist the Catalan powerhouses are not relenting in their pursuit, via Football Espana:
News of a winter move would be odd considering Barcelona would still need to beat the offers said to have been made in the summer. This is unlikely given he'll be cup-tied in the UEFA Champions League and therefore not hold as much value to his prospective buyers.
Coutinho missed the start of this season after a controversial summer transfer window at Anfield, but the playmaker is now nearing his best again and was recently nominated for the 2017 Ballon d'Or, per BBC Sport's Simon Stone:
Gallagher's report noted how news of an agreement between Liverpool and Coutinho goes against the notion he'll serve the remainder of his contract until 2022, something the Reds have been adamant about throughout.
Liverpool fan account Empire of the Kop is counted among the doubters:
Coutinho's presence at Anfield will also be crucial now that star attacker Sadio Mane has been ruled out of action due to a hamstring injury. Gallagher suggesting the winger could be absent for 10 weeks.
Barcelona might struggle to raise the winter funds it would require to tempt Liverpool into selling such a key figure halfway through the season, although claims of a "promise" between them and Coutinho would seek to unsettle any harmony.