The Scot was relieved of his duties on Tuesday morning only 10 months into a six-year contract at Old Trafford, having presided over the club's worst campaign in the Premier League era.
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But speaking to the Guardian, the German said: "Man Utd is a great club and I feel very familiar with their wonderful fans. But my commitment to Borussia Dortmund and the people is not breakable."
Klopp has established himself as one of Europe's most sought-after managers after leading Dortmund to back-to-back Bundesliga titles and a Champions League final.
Other front-runners to succeed Moyes are Netherlands boss Louis van Gaal, Atletico Madrid manager Diego Simeone and Real Madrid coach Carlo Ancelotti.
Van Gaal is also wanted by Tottenham to succeed Tim Sherwood, but last week Goal reported that the Dutchman was taking time to weigh up his options having been linked with United.