Yorkshire coach Gillespie was widely expected to get the job but new England cricket director Andrew Strauss has opted for the 52-year-old Bayliss who led Sri Lanka to the 2011 World Cup final.
"The ECB have said they're speaking to their preferred candidate," the 40-year-old Gillespie told Sky Sports.
"I've spoken to Andrew Strauss and I'm not that preferred candidate. So that's fine.
"It would have been a good job to have, there are exciting times ahead for English cricket and it would have been a great challenge but it's not be," the former Australia fast bowler added.
"As I've said I've got a wonderful job with Yorkshire and with Adelaide Strikers and I'm looking forward to continuing that work."
Bayliss has also coached Australian state side New South Wales and Kolkata Knight Riders in the Indian Premier League.
The five-match Ashes series against Australia starts on July 8.

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