Costa has not been far from the headlines and found himself the talking point again in Tuesday's 1-1 draw with the Reds at Anfield, with some feeling the Spain striker went to ground too easily under a challenge from Joel Matip in the penalty area.
The former Atletico Madrid star assumed responsibility for the penalty, but saw his effort denied by Simon Mignolet 14 minutes from time.
Referee Mark Clattenberg's decision to award the spot-kick was one of the main talking points, but while Klopp admits he would not enjoy a friendly relationship with Costa, he refused to condemn the striker without seeing the incident again.
"If I had played against Costa I could never be friends [with him], that is how it is," Klopp told reporters following the draw with the Premier League leaders.
"But when you have him in your team it is much more fun. He is a warrior. What [Antonio] Conte is doing with Chelsea is outstanding, but Chelsea without Costa this season [who knows where they would be?].
"He is not the nicest guy on the pitch but I saw no real big incident and until someone tells me something...
"If someone tells me it was a dive maybe I will be angry Wednesday but that would be wrong decision what, number 27? But it does not make it better."