The 34-year-old American had agreed a price with the Hemmings family to buy PNE in February.
But it is understood that two revised offers, both reduced in price, had been made more recently and any deal was now off.
Included in the package for the proposed purchase was Deepdale, Euxton, Springfields and the land at Ingol on which the club wanted to build a training ground in 2017.
Kirchner’s period of exclusivity ended at midnight on Thursday, with him having been doing due diligence in the last few weeks.
North End are the second Championship club he has tried to buy, having pulled out of a deal to purchase Saturday’s opponents Derby County last year.
At a press conference on Friday, PNE director Peter Ridsdale read a statement which the club have released to outline recent events.
Ridsdale said: “There has recently been public speculation with regard to the future ownership of Preston North End Football Club.
"Since the untimely death of Mr Hemmings last October there have been a number of enquiries with regards a potential change in the ownership of the club.
"In February an acceptable offer was received from one interested party and a period of exclusivity and confidentiality was entered into. This was to enable due diligence on the club to be done and all the required approvals for change of ownership to be sought from the Football League by the potential buyer.
"This exclusivity period has now ended. To date, there has not been a confirmed offer at the previously agreed price made to the owners.
"Neither has there been any of the required submissions made to the Football League for consent to change of ownership.
"As of today we are not engaged with any party.
"The Hemmings family have been dedicated owners of Preston North End for many years and remain committed to the future management and funding of the club.
"Speculation at any time can be distracting not just for the manager and players but for all employees.
"Therefore we can assure that following this statement everyone will get behind Ryan Lowe and the team as we enter the last eight games of the season.”
Following the reading of the statement, Ridsdale spoke further on the subject.
Ridsdale said: “I don’t want anyone reading into the statement that at any time either the Hemmings family or anybody in the football club have done anything other than to co-operate with any party who have a genuine interest in buying the football club.
"The fact this particular situation has now ended has not been for any reason due to an act by anyone in the Hemmings family or indeed within Preston North End.
"The period of uncertainty that has been in place for the last few weeks has not been helpful. It has meant a number of things we would liked to have done, such as season tickets for next year etc, have been put on hold.
"As of today it will be back to business as usual. There will be frenzied activity over the next few weeks to make sure we can all look forward not only to the last eight games of this season but also to the season which start at the end of July.”