The two German managers meet for the first time in the Premier League when Liverpool welcome Manchester United to Anfield on Tuesday.
Klopp has crossed paths with the former RB Leipzig, Hoffenheim and Schalke 04 manager several times in the past with the Liverpool manager's sides triumphing in just two out of 13 meetings.
Liverpool will be looking to move top of the table with a win while the Red Devils will want to enhance their top four credentials.
Asked how his relationship with Rangnick was ahead of the match at Anfield, Klopp replied: "On hold.
"No, we didn't have contact since he was at United. I think that's mutual respect. I respect his job; he respects my job.
"I cannot make it a Klopp-Rangnick or Rangnick-Klopp game, I don't want to. I respect him for everything he did during his career – he did incredible jobs wherever he was.
"He took a difficult one at United, that's clear. There's big expectations with these things, big expectations but no time to get there. In our business, it's like this.
"You can see the changes he made and the parts he improved, but that's it. When I prepared the United game, I didn't think about Ralf in that moment. You watch the games and you prepare for this team.
"It's not about Ralf or me; it's a very important football game, a very, very important football game. The managers probably will not score the decisive goal."
Liverpool beat Manchester United 5-0 in the corresponding fixture at Old Trafford earlier this season when Ole Gunnar Solskjaer was in charge.
