The England and Wales Cricket Board is in exclusive discussions over the England coach role, with a candidate understood to be Trevor Bayliss.
Reports in Australia suggest the New South Wales coach, 52, is set to be appointed as Peter Moores' successor.
Jason Gillespie was expected to take the job after talks with director of cricket Andrew Strauss last week.
But the Yorkshire coach told BBC Sport that Strauss had since informed him he was not the "preferred candidate".
"I spoke to Andrew this morning," former Australia fast bowler Gillespie said on Monday. "He said they've got a preferred candidate they're speaking to. It would have been a tough decision for me, but I don't have to make it. That's absolutely fine, no worries at all.
"Throughout the whole process the ECB have been very good. I certainly haven't been led down the garden path. It was made clear to me there were a number of candidates.
|Former England captain Alec Stewart on Test Match Special:|
|"Trevor Bayliss hasn't just suddenly appeared. He has got a good track record behind him - he coached Sri Lanka to the World Cup final. But he hasn't got a lot of international playing experience - he didn't play for Australia. Gillespie appeared to be the favourite, but Andrew Strauss said he would do a thorough job and then make a decision. And that's what his role is."|
"Everyone who has worked with Trevor has had nothing but very positive things to say about him. He's worked with [England assistant coach] Paul Farbrace in the past with Sri Lanka and I'm sure they would be delighted to work together again.
"Farbrace is a fantastic coach and is certainly somebody England should keep."
Bayliss was appointed New South Wales coach for a second time in 2013 and has twice won the Sheffield Shield with the Blues.
The Australian has also had considerable success in his role as coach of Twenty20 sides the Sydney Sixers and Kolkata Knight Riders, winning the Australian Big Bash and Champions League with Sydney in 2012 and the Indian Premier League title with Kolkata Knight Riders in 2012 and 2014.
But he is perhaps best known for leading Sri Lanka to the 2011 World Cup final in Mumbai, where they narrowly lost to India, with Farbrace - England's stand-in head coach - as his assistant.
Farbrace told Sky Sports: "He's an old-fashioned cricket coach who likes working in the nets. He's quiet but when he says something it counts.
"He's a good man who is very knowledgeable. He has experience all round the world. I want to be involved in the future, whatever the role is."
Former England batsman Ed Smith, who played under Bayliss when he coached Kent briefly in 2003, told Test Match Special: "He was excellent, understated and got stuck in to work with the players.
"His playing career may have influenced his coaching style as he was in a very strong New South Wales side and could slip in under the radar. In coaching, he is happy to do the same and he is a nice guy."
|Ex-England spinner Phil Tufnell on Test Match Special:|
|"From what I've heard, he's a laid back kind of character who won't be putting his face up front - he'll let the guys and the captain get on on with it. It could be a good announcement."|
Gillespie's former Australia Test team-mate Justin Langer had also been named as a contender for the role of England coach, but the 44-year agreed a two-year extension to his contract as coach of Western Australia earlier this month.
Bayliss was also considered for the job of England coach in April 2014 before Moores was appointed for a second time following the resignation of Andy Flower.
Speaking to Test Match Special on BBC Radio 5 live, former England captain Michael Vaughan said Bayliss had a "good track record", but his appointment would be a "big surprise" given the strength of Gillespie's candidature.
"Would Trevor Bayliss be a good coach for England? His pedigree suggests he would be," said Vaughan. "I think either personality would be good for English cricket, but if you gave me the opportunity to go either way I would definitely go with Gillespie."