Coutinho, 25, was the subject of a long pursuit from the Catalan giants in the summer transfer window and made his desire to swap Anfield for the Camp Nou abundantly clear to Jurgen Klopp's side when he submitted a transfer request.
The Brazil international's wish was not granted and he remains a Liverpool player, but Barcelona are set to reignite their attempts to sign the former Inter Milan starlet with club chief Oscar Grau saying earlier this week that the Blaugrana are now "prepared" to sign Coutinho.
Barcelona are reportedly planning to offer a €110m financial package for Coutinho, who has scored twice and provided one assist in three Premier League matches, and Adam, who briefly played for Liverpool under Kenny Dalglish, thinks his former club should cash in on a player he sees as be one of the best in the world.
The Stoke midfielder thinks the fee touted for Coutinho could allow Liverpool to completely revamp their much-maligned backline, which is set to be tested to its limits against high-flying Manchester United on Saturday (14 October).
"This is what happens when you've got one of the best players in the world," Adam told talkSPORT. "It's going to just see how long the Liverpool owners stay strong – can they afford to not let him go in the January window?
"I think if they're nowhere near winning the league, he will go. The money they're talking about - £120million – that's a rebuilding job!
"That will buy them the four defenders and a goalkeeper they probably need."
Coutinho may be wearing Barcelona colours in the not-too-distant future but Liverpool will certainly rely on him against United especially when taking into account to absence of Sadio Mane, who could miss the next six weeks with a hamstring injury.
Coutinho has clocked up a lot of air miles in recent days due to the international break but managed to take part in training at Liverpool's Melwood training base on Thursday along with his teammate for club and country Roberto Firmino, who will certainly lead the line against United at Anfield.