The German has spoken to Edwards, with whom he had a successful relationship as the club's sporting director until he left in 2022, but there will be no dramatic U-turn.
"We had that conversation, (but) that is not a subject to talk about," Klopp told reporters. "Can you imagine I changed my mind?"
"It's like, 'Never ever another club in England' and next year I signed for our neighbours. I think before I say these things.
"For me it is the best club in the world and I am still leaving. I just want this club to do as well as possible with the best people in charge and Michael is a top choice.
"We spoke about a lot of things, what I think about players, what needs to change and a really good talk. I am really happy. I want it to be the best possible place after I leave. I think it is a top solution and our conversation was obviously great."
Klopp was speaking ahead of the second leg of Liverpool's Europa League last-16 match against Sparta Prague on Thursday. His team, chasing four trophies, are 5-1 up after the first leg.
The recently crowned League Cup winners are level with Arsenal on 64 points at the top of the Premier League and play Manchester United in the FA Cup quarter-finals this weekend.
But Klopp said there was still a long way to go.
"The boys are quite consistent in recent weeks but it's a long run-in in all competitions and we are not even close to the finish line," he said.
"I can't see it. I can only see Sparta Prague wants to put things right and we have to play a good football match because it's our home game and our stadium. It's our competition. We want to make this our competition and go as far as possible."
