McCullum was removed from the Test coaching position last week and former Zimbabwe international Flower emerged as the leading candidate to take over.
But Flower, who previously led England between 2009 and 2014, is currently in charge of IPL side the Royal Challengers Bengaluru as well as Hundred team the London Spirit.
ECB managing director Rob Key spoke to Flower about the job.
But the 58-year-old cited his IPL commitments, which would overlap with the early weeks of the English cricket season, as the main reason why he does not wish to be considered.
“Obviously that is a topic that’s being talked about at the moment. I have spoken with the ECB. We’re all aware of the vacancy for the head coach job of the England national team,” he told reporters on Friday.
“I have spoken with Rob and the ECB on that topic. The bottom line for me is that I’m very happy in the work that I’m doing at the moment.
“I work for a couple of really good organisations, I’ve got really good teams around me, really good people around me. I’m really comfortable with what I’m doing at the moment.”
Flower previously led England to No 1 in the world rankings and a stunning Ashes win in Australia in 2010-11 and is held in high esteem by the ECB.
His decision is a blow to the ECB as they seek to move on from a challenging period.
A 2-1 Test series defeat at home to New Zealand, after the 4-1 thumping in the Ashes, was followed by the retirement of Ben Stokes as captain and McCullum’s removal from the Test role.
“I’ve worked with England before, as you all know. I had an amazing time when I had the privilege to be England head coach and represent England as one of their leaders a number of years ago. I remember those years really fondly,” he said.
“It would be a privilege for me or anyone else to be the Test coach. But for me at this time, I’m really comfortable with what I’m doing. I’m going to stick with doing that.”
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