ECB chief hints Giles will succeed Flower
England batsman Kevin Pietersen pictured during the third day of the fifth Ashes Test against Australia in Sydney on January 5, 2014 - by Saeed Khan
Flower resigned on Friday to allow the team to rebuild after their disastrous tour of Australia, where they lost the Test series 5-0.
However, he is remaining a selector "for the time being", with British reports saying the decision to stand down was his alone and not prompted by the Ashes humiliation.
Flower had already ceded coaching control of England's one-day team to former England spinner Giles, and said he had come to the conclusion that a man in his position needed to be "responsible across all formats".
Clarke suggested Giles could take over all three formats, without putting a timeframe on any appointment.
"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," he said in Melbourne.
"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 (England cricket's managing director) leads the process."
England's next Test match is not until the northern hemisphere summer, when they host Sri Lanka.
Last month British press reports, denied by Flower, suggested he was not prepared to carry on as England coach so long as Kevin Pietersen remained in the team.
Clarke refused to be drawn in whether the controversial batsman had played his last Test.
"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, quite rightly, on looking at the coaching strategy as far as Andy is concerned."
Pietersen has signalled he intends to keep playing international cricket until at least the 2015 Ashes, with a clearer indication of his future coming this week when England name their squad for the one-day series in West Indies and World Twenty20 in Bangladesh.
England play their final Twenty20 international in Sydney on Sunday.
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