A 3-1 win over Manchester United - the club's first in nine attempts and Klopp's first as Reds boss - returned them to the summit after Pep Guardiola's side had moved above them on Saturday.
Liverpool have a chance to extend their one-point advantage further as they play Wolves on Friday night but Klopp is focusing on what his side do and not what their rivals are up to.
"We ignored it completely. I didn't mention it one time," he said. "We know the table, just are you focused on it or not. We played tonight against Man Utd and not Man Utd and City.
"When we eat and train together we are not saying 'Did you see what City did?'
"We are focused on what we need to do and will there come a moment in the season where we are still around them and we start hoping they drop points or whatever.
"But at the moment we respect them a lot and they respect us. We meet them on January 3 and then we will think about them."