English media said Flower was ready to quit unless he was given guarantees that the polarising batsman would not be selected to play under him in the fallout following the 5-0 Ashes series humiliation at the hands of Australia.
It follows rumours of a breakdown in their relationship, reportedly sparked by Pietersen making himself unavailable for one-day international matches last year in order to play in the lucrative Indian Premier League.
Pietersen, 33, who finished as England's highest scorer in the series with 294 runs at 29.40, has posted a series of tweets stating he wants to remain part of the England set-up, insisting he is "determined to help regain the Ashes in 2015".
Flower said in a statement that no snap decisions would be made despite the humbling by England's oldest rivals.
"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," he said.