The pair clashed in last week's draw at West Ham.
And Klopp said on Friday: "There's no problem. We are absolutely fine with it. It's a non-story."
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He continued: "I think we have the right to deal with these things completely independent of any expectations from the outside.
"If we didn't know each other for that long I am not sure how we would deal with it but we have known each other for that long and respect each other so much that it's really no problem.
"The best situation would be everyone is in the best place, we win the games and score loads of goals then yes, the situation probably would not have been like that because Mo wouldn't have been on the bench in the first place. It all depends on each other."