Several national newspapers reported that Flower was willing to walk away from his job if Pietersen remained in the long-term plans of the England and Wales Cricket Board (ECB).
Flower and Pietersen have endured flashpoints before, most notably in the 2012 summer when Pietersen was left out of the England team after his texting controversy and abrupt decision to retire from one-day internationals.
But claims that Flower is now ready to move forward without Pietersen - after the 45-year-old coach was given ECB backing to retain his job in the wake of the Ashes debacle - were quickly dismissed.
Flower described suggestions he had issued an ultimatum as "totally inaccurate" in a press release issued by the ECB.
Flower added that any decisions over the futures of individual players or support staff would not be made so soon after an emotionally taxing series.
"Following speculation in the media today I feel it necessary to reiterate much of what I said in my recent press conference," Flower said in the statement.
"It would be sensible and responsible to review the tour in a calm and logical manner before assessing our options for the future and planning ahead.
"I repeat that neither I nor the wider ECB leadership group have made any decisions as to the future involvement of any individuals in the playing group or in the support staff.
"The reports that I have issued an ultimatum of some description to the ECB are totally inaccurate."
Pietersen too felt the need to comment on the newspaper reports, via Twitter, saying he was "shocked and saddened" his England future had again been called into question.
The right-hander had only on Tuesday re-affirmed his commitment to England - amid claims he might opt to retire - saying that he intended to try and win back the little urn in 2015.
Pietersen has also previously stated he would like to become the first England player to reach 10,000 Test runs.
"I am shocked and saddened by reports in the media today concerning my future with England," Pietersen tweeted.
"I wish to repeat my strong desire to continue playing for my country, and to help us regain the Ashes in 2015."
Despite the insistence of both coach and player the matter is unlikely to go away any time soon.
After the Ashes whitewash was confirmed in Sydney last week, Flower revealed his desire to build a "new era" while also pointedly warning that "more pain" would likely be suffered before results turned around.
The Zimbabwean had overseen a hat-trick of Ashes successes before this summer, while England have been top of the rankings in all three formats during his almost five-year tenure.
Pietersen has played a significant role in that, however, his working relationship with Flower has been under scrutiny since the controversial 2012 summer.
Pietersen was ostracised from the team by Flower after the mercurial batsmen took to YouTube to, amongst other things, back track on his ODI retirement.
Pietersen was then left out of the final Test of the summer after sending 'provocative' texts to South African rivals about then skipper Andrew Strauss.
Pietersen was subsequently 'reintegrated' back into the England squad in time for the India series, reportedly with new captain Cook as the driving force, and played a key role in an historic 2-1 series win.
England skipper Michael Vaughan believes the loss of either would be a major blow, but concedes something is clearly wrong.
"Andy Flower has seen all the headlines. He might not have said exactly what is reported, but there is clearly an issue between him and Kevin Pietersen," Vaughan told BBC Radio Five Live.
"The best player, the maverick, the X-factor player is stood on the boundary during games. He is never involved in any of the team discussions.
"The two can carry on. Both of them and the team need space away from each other because it has been such a pressurised tour.
"Give it a week or so and take a little bit of time to breathe, then have a mature meeting.
"Let's get them both together and try and get English cricket moving forward because it will be a great shame if Kevin Pietersen never represents England again.
"The dust needs to settle, then people need to bang heads together and get them in a room together and get it sorted out."
Flower and Pietersen will at least be able to get away from their travails in Australia as both men will be absent from the upcoming limited overs series.
Flower has ceded control of the shorter formats to Ashley Giles while Pietersen has been rested for the tour-ending matches, which begin with the first ODI in Melbourne on Sunday.
Despite their down time there are more potential flashpoints on the horizon - most significantly Pietersen's Indian Premier League commitments.
His signature will be highly-prized at next month's IPL auction, and at 33 - with a dodgy knee - Pietersen may decide to put Twenty20 earning power and profile ahead of pleasing the ECB at every turn.
Debate is therefore almost certainly set to revolve around Pietersen's availability at the start of this year's domestic season, and whether he will have appropriate preparation for an ODI series in May and then Tests in June against Sri Lanka.