Paul Downton, the managing director of the New England and Wales Cricket Board, will begin the task of finding a successor after Giles and the England team return home from Australia today.
"I'd be very interested in doing the job, definitely," Giles said, after his side finished their morale-shattering tour with an 84-run defeat in Sydney to concede the Twenty20 series 3-0. "I'm not going to deny that and I'm sure I will be applying for the post."
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Giles revealed he had already spoken to Downton following Flower's decision, which came as a surprise to him. The 40-year-old is, though, not taking anything for granted after enduring a chastening experience of his own in Australia.
Defeat in Sydney condemned England to a second series whitewash of the winter, following their 5-0 Ashes embarrassment. They also lost the one-day international series 4-1. Giles is therefore reluctant to think too far ahead with a limited-overs tour to the West Indies and the World Twenty20, which starts in Bangladesh on March 16, foremost in his thoughts. "I've not given him my cv yet," he said. "At the end of the day I think it is important that I control what is coming up in the next couple of months.
"If I have to put an application in over the next couple of weeks then I'll think about that and get it done. Results will talk as well and I've got a really big series in the West Indies and more importantly the World Cup in Bangladesh. Our record in the sub-continent for limited-overs cricket isn't brilliant so it is a good challenge. We're pretty much at base level right now. We have a lot of work to do and before that we have a lot of talking to do about which squad we take."
Downton has time on his side before any decision on the new head coach needs to be made, with England's next Test not until June when they host Sri Lanka.
The former India and South Africa coach Gary Kirsten has been tentatively linked, and Giles knows showing he can turn fortunes around in the next two months can boost his prospects.
"I'm not silly, if it goes out to a process other people are going to apply," he said. "It's one of the biggest jobs in cricket and I'd apply for it because I want to do it. I've been proud to coach the one-day side. To do the whole job would be a fantastic."