Klopp, who left Liverpool at the end of last season after a nine-year stay on Merseyside, is one of many names linked with taking over from Gareth Southgate.
Southgate led England to back-to-back European Championship finals, failing to win in both and stepped down from his role after their defeat to Spain at Euro 2024.
The last time the Three Lions employed a foreign manager came back in 2008, when Fabio Capello was announced as Steve McClaren’s replacement.
Klopp was asked at an International Coaches’ Congress in Wurzburg whether he had been offered a way back into management since leaving Liverpool.
“At the moment, there is nothing at all in terms of jobs. No club, no country,” Klopp said.
“England? That would be the biggest loss of face in the history of football if I said I’ll make an exception for you.”
England’s first game following Southgate’s departure will be against the Republic of Ireland in Dublin on 7 September in the UEFA Nations League.
Klopp said his reasoning for leaving Liverpool was because he was “running out of energy” having helped the Reds win eight major honours during his time at Anfield.
However, the 57-year-old did not rule out a return to the dugout in the future, expressing his desire of working in football again.
“Let’s see what it will look like in a few months. Nothing is coming through at the moment,” he said.
“As of today, that’s it for me as a coach. I didn’t quit on a whim, it was a general decision.
