Kirchner had engaged with PNE fans on Twitter when asked his view on the club posting a near £13.6m loss for the last financial year.
The 34-year-old, who tried to buy Derby County last year, was asked whether he had an interest in buying PNE.
His reply was: "We will have something to share soon… different situation than Derby. Public pressure not useful in negotiations."
PNE's statement read: "In response to today's rumours with regards to ownership of the club, we can confirm that since Mr Hemmings' untimely death we have had a number of expressions of interest in the club, including in recent weeks.
"Unless or until there is anything more definitive to say, we will not make any further comment."
Kirchner watched North End's game against Huddersfield Town at Deepdale a fortnight ago, that coming during a trip to Europe following time in Dubai where he had sponsored a golf tournament.
He was reportedly at Deepdale again on Tuesday night for the goalless draw with Nottingham Forest.
On Wednesday afternoon, he posted on Twitter that he was flying home to Texas for a break.
PNE's financial report for the year ending June 2021 was filed with Companies House on Wednesday morning.
It showed a loss of £13,597 for a period which covered the delayed end to the 2019/20 season and all of the 2020/21 campaign which was played behind closed doors.
Turnover decreased to £10.5m in that time due to no money being taken at the turnstiles but the wage bill increased to more than £22m.
Trevor Hemmings passed away last October at the age of 86. He had owned PNE outright since the summer of 2010.
PNE are now controlled by his family, with Craig Hemmings having been chairman since July 2019.
Like the majority of Championship clubs, North End are open to offers to buy them and that was always the case during Trevor Hemmings' ownership.
Kirchner's bid to buy Derby from their administrators developed at the back end of last year but ended shortly before Christmas.
He watched a number of their games alongside former Manchester City chief executive Garry Cook and Paul Stretford - the agent of Derby manager Wayne Rooney.
Kirchner was with Cook for PNE's game against Huddersfield, it being Cook who arranged the executive box at Deepdale from where they watched the match.