If it were up to Klopp who got a contract then Gini would have got what he wanted a long time ago. Its not up to him though and i'd say the meeting was more or less to find out where his head is at. Edwards knew they were meeting up and if they had an improved offer they would have given it then and we would be reading about that instead of him hoping productive talks will lead to an offer of a contract extension.
I can remember the same stuff being wrote that Emre Can could still sign a deal heading into his final year and look how that turned out.