His talents were/are wasted by and large under Rodgers and even Low for the German national team. Under Rodgers he bounced around in midfield, fullback and part of a back three. That's not good for any player's development. Under Klopp he's clearly a midfielder. However, his natural position seems to be a 6, where he played behind Henderson. The other CM positions were occupied by Wijnaldum and Lallana, who are both much better suited for what Klopp is trying to do.
Can has always been immensely talented. The problem was trying to find a place for him. He's a bit like Ross Barkley, but significantly better on the ball. The problem may be that he's not very bright. Or maybe he doesn't know what to do with his talent. But he generally makes poor decisions in the final third. Even that incredible kick was a "poor" decision. He could have knocked the ball down off his chest and either looked to shoot or pass. Instead, he went for the once in a lifetime shot. You can't argue with the result, but it's a reflection of his mentality.
He's really not a perfect fit for a club that looks to create with movement and passing. He's probably better suited to play for (I hate to say it) like a Mourinho.
Liverpool need a much bigger club next year, so it's important that they sign him to an extension. Unfortunately, that probably isn't going to happen.