The midfielder was the star of the show for Liverpool in the opening day win.
Liverpool's Philippe Coutinho celebrates scoring their third goal with Nathaniel Clyne
Coutinho was the star of the show on the opening weekend, scoring two goals in Liverpool’s 4-3 win over Arsenal at the Emirates.
One of those goals was a sumptuous free kick past Petr Cech that is already a contender for goal of the season.
His display was the latest impressive one from the Brazilian, who has shown marked improvement under the guidance of Klopp since he took charge last October.
Liverpool's Philippe Coutinho scores their first goal with a free kick
The inevitable comparisons to former star Luis Suarez are already being made but Klopp has questioned the wisdom of making it.
“After one game - and not because it's Phil - but what are we doing?" he told the Mirror.
“Ask Suarez if he ever scored a free-kick like Phil [did on Sunday]. I'm sure he scored many great goals, but not a lot like this. But we are all different, so why should we compare one good player with another?"
Liverpool's Philippe Coutinho celebrates scoring their first goal with teammates
It remains to be seen if Coutinho can build on his strong start to the season and enjoy a big season with Liverpool.
There is no denying his quality but he must now prove it on a regular basis, with consistency having been something that has stopped him hitting the next level in his game.
Should he find that and help the Reds push for the top four place they crave, then those comparisons to Suarez are only likely to increase in number.
Luis Suarez Barcelona celebrating