"I'd be very interested in doing the job, definitely," Giles said in an interview with Sky Sports.
"I'm not going to deny that and I'm sure I will be applying for the post.
"If I have to put an application in over the next couple of weeks then I'll think about that and get it done."
Giles has won 15 of his 38 matches in charge but he does not expect to be the only candidate interested in taking over from former Zimbabwe wicketkeeper-batsman Flower.
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"I'm not silly, if it goes out to a process other people are going to apply," added Giles who took 143 wickets during his test career with England.
"It's one of the biggest jobs in cricket and I'd apply for it because I want to do it.
"As someone who was very proud to play for England I've been proud to coach the one-day side. To do the whole job would be a fantastic opportunity, but it's hard work as well."
Flower resigned after England's 5-0 Ashes whitewash. England also lost the one-day series 4-1 to Australia.
(Reporting by Michael Hann; Editing by Rex Gowar)
