The Brazil international hit a purple patch in late October and early November with four goals in three matches, including one in the 4-1 thrashing of Manchester City, and is on track to beat the eight goals he got last season, which was his best-scoring campaign at Anfield.
He believes he has already progressed under Klopp and the team are also improving.
"It feels like we are moving in the right direction under him and we believe we can fight for the big prizes and enjoy some special moments with the fans," Coutinho told World Soccer magazine.
"In training, we are working hard and enjoying his methods, which are helping to make us better players.
"Klopp has put his ideas forward and they are helping to make me an even better player.
"I have been lucky to work under some fine managers already in my career and they have each added an element to my game.
"The likes of (Rafael) Benitez, (Mauricio) Pochettino and Dunga are great coaches but I will always have a special gratitude to Brendan.
"He believed in me and brought me here. He gave me the opportunity to play for such a great club."
Source: PA