Klopp has stated this past week, before and after victory over Newcastle United, that his players have not missed Coutinho's influence on the pitch since his January sale.
The claims have left Coutinho unimpressed and he has texted some former team-mates to tell them about his feelings.
He was unhappy at what he has perceived as criticism, saying that the squad are more of a team without him.
The report goes onto say that Coutinho and Klopp endured a frosty relationship towards the final days of his time at Anfield.
Klopp repeated to the media on many occasions that the Brazilian would not leave the club, which was not received well by Coutinho.