Coutinho, who moved to Anfield from Inter Milan, has already made a positive impact on Merseyside, with Enrique insisting that he can become as good as striker Luis Suarez.
The 27-year-old told the Liverpool Daily Post: "Luis had a really good year after just six months here before. Now you can see the real Luis, with how many goals he scores.
"With Coutinho, it's going to happen the same I think. You can see how well he is doing but I think he's going to improve a lot more – if he improves after what he has been doing already he is going to be a top player for us.
"He's a really calm player; he doesn't talk much but he's always joking. I really like him."
The Brazilian has scored twice in eight Premier League appearances for Liverpool.