ECB chairman Giles Clarke hinted ODI and Twenty20 coach Ashley Giles was the leading candidate to replace Flower as Test mentor as the fallout from England's 5-0 Ashes humiliation continues.
Clarke also gave his unequivocal support for Alastair Cook continuing on as England captain despite his personal capitulation against Australia.
However, Clarke refused to be drawn on whether controversial batsman Pietersen had played his last Test for England.
There was widespread speculation in the British press that the relationship between Flower and Pietersen had reached breaking point and that they could no longer continue working together.
Pietersen has signalled he intends to keep playing international cricket until at least the 2015 Ashes in the UK, and it seems England are holding off on making any decision on their star's future.
A clearer indication will come on Thursday when England name their squad for the one-day series in West Indies and World Twenty20 in Bangladesh.
"I have spent zero time on him (Pietersen) or whatever he or the selectors are choosing to do," Clarke said.
"I have been focused on ICC business and Paul Downton (England cricket's managing director), quite rightly, on looking at the coaching strategy as far as Andy is concerned."
Chairman Clarke said Flower had stepped down of his own accord and wasn't pushed.
England are planning to find a new senior role for him within their coaching and development structure.
Flower oversaw three Ashes triumphs for England as well as a World Twenty20 win.
Clarke endorsed former England spinner Giles to take over all three formats.
"We would all agree he is a very strong candidate. We have the highest regard for him as a man and coach of great integrity and capability," Clarke said.
"He played a lot of cricket for England and is respected in the game. It may well be that other outstanding candidates emerge as Paul Downton leads the process."