Back in April, Kirchner was named as the preferred bidder, but failed to meet Friday's deadline to prove he was in the right position to complete the takeover.
A spokesperson on behalf of Derby's joint administrators said: "The joint administrators can confirm that today, Mr Kirchner has withdrawn his offer to acquire the business and assets of The Club.
"We are aware that some will be concerned by this news, however, the joint administrators wish to reassure The Club's staff, players and supporters that they are continuing to actively engage with a growing number of interested parties, each of whom have a real willingness to complete a deal as soon as possible."
One man who has retained his interest in purchasing the club is former Newcastle United owner Mike Ashley.
Derby's relegation from the Championship was confirmed last April as Wayne Rooney's men unsuccessfully battled on after being docked 21 points for financial issues.
Kirchner exchanged contracts with Derby's administrators Quantuma in May and it had been expected that the American's takeover would be completed.
The English Football League released a statement on Sunday expressing their concern that the protracted bid to take the club out of administration was becoming "a real risk to the integrity of next season's competition".
The joint administrators said in their latest statement they were continuing to run "a competitive bidding process", saying: "Bids should be best and final and not contain any referential element.
"Clearly, any bid is subject to interested parties entering into an NDA (non-disclosure agreement), accessing the data room, and undertaking their own due diligence. Of the parties we are engaging with, some are more progressed in this process than others."
Derby suffered relegation to the third tier for the first time since 1986.