Moyes was relieved of his duties on Tuesday morning after failing to live up to lofty expectations at Old Trafford, lasting just 348 days of his 6-year contract.
The Red Devils confirmed that Ryan Giggs will take charge of first-team affairs while the board looks for a permanent replacement, with Klopp believed to be high on their wishlist.
However, both Dortmund and their boss have categorically stated that Klopp would not be leaving the Westfalenstadion for Manchester any time soon.
BVB director of communication Sascha Fligge told ESPN FC: “Jurgen Klopp already dismissed rumours linking him to Barcelona on our official homepage on Saturday.”
In addition, the German tactician put pen to paper a new deal with the club in October, extending his stay until 2018.
At the end of last season, Klopp had also been linked with the United job as a successor to Sir Alex Ferguson, but Fligge said that Dortmund’s position remains the same.
“We’ve already had this last year, but it’s final, even if some people don’t want to believe it,” he added.
The former Mainz boss told The Guardian: “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.”