Gillespie was the clear favourite to get the role in place of the sacked Peter Moores.
But England are believed to be on the brink of appointing Gillespie’s fellow Australian Trevor Bayliss.
Speaking at Taunton today, where Yorkshire are playing Somerset in the County Championship, Gillespie confirmed he had been turned down for the post by England director of cricket Andrew Strauss.
“I spoke to Andrew this morning, and he said they’ve got a preferred candidate they’re speaking to,” said Gillespie, who conducted two meetings with Strauss last week.
“I said, ‘That’s fine, no worries at all.’
“It was made very clear to me that there were a number of candidates that the ECB were speaking to.
“I had a good meeting with Andrew and Tom Harrison (ECB chief executive), and they were very professional and thorough throughout the whole process, so I’ve got no qualms whatsoever.”
Gillespie said it would have been a difficult decision to leave Yorkshire, whom he led to the County Championship title last summer.
Yorkshire have won 22, drawn 27 and lost only three of 52 Championship games under the former Australia fast bowler.
“It would have been a difficult decision to leave Yorkshire,” said Gillespie.
“As I’ve said all along, I love my job at Yorkshire - it’s a fantastic role.
“I’ve got wonderful support from everyone at the club, our supporters are brilliant and the players are fantastic.
“It would have been a tough decision to leave, and I’ve also got this new role with the Adelaide Strikers in the Big Bash League that I’m very excited about.”
England are set to turn to Bayliss, who was considered for the England job when Moores was appointed last year.
The 52-year-old is the coach of New South Wales and has previously led Sri Lanka to the World Cup final.
Bayliss’s No.2 at Sri Lanka was Paul Farbrace, the England assistant coach who is presiding over the current series against New Zealand.
Now it seems the pair are about to link up once more.