The Brazil international arrived at Anfield in January after making the move from Inter Milan and has scored two goals in 10 appearances for the Reds, and created countless chances.
Speaking to the official matchday programme, Leiva said: "Philippe is a young player but he has got a lot of experience because he spent two years in Italy and six months in Spain so he knows how things work in Europe.
"Of course the Premier League is a different league but he has been fantastic for us since he came.
"For sure, he will only get better because he is very young and works very hard. We are just delighted that he came here and is having the chance to show his quality. That is maybe what he didn't have in Italy with Inter."
Fellow Brazilian Leiva, who has been at Anfield since 2007, also believes the presence of a trio of South Americans has helped Coutinho settle in so quickly.
He added: "He has settled quickly and has myself, [Sebastian] Coates and [Luis] Suarez to help him feel comfortable and understand a bit more. I'm sure the fans are really looking forward to seeing a full season from him next year just as I am."