The Brazil international pledged his future to the Reds on Wednesday by signing a new contract at the club, ending speculation over a possible move away from Anfield.
Sky sources understand Coutinho has penned a deal that will keep him at the club until 2022 and that no release clause has been inserted into the contract.
“This is wonderful news and I know everyone associated with LFC will be delighted when hearing this today,” Klopp told the club’s website.
“I think everyone knows what a great footballer Phil is, that is not in question – but not everyone sees what an incredibly positive character he is and what a big influence he is on the dressing room.
“I knew of Phil before I came to Liverpool and I was well aware of what a talent he was, but since arriving here I have not only witnessed his ability up close, but also his ever-continuing development. He is truly world-class – in that very top bracket.
“The fact he wants to stay here and be part of what we are looking to build and develop shows his personal commitment is to make himself better and be an integral part of something that is very special.