Moores was in contention along with South African Mickey Arthur and Australians Dean Jones, Tom Moody and Jamie Siddons for the post.
A source said Peter Moores is a front runner for the job.
Ex-England coach voices thoughts on his work with the team during his tenure.
If Gillespie takes up the job, he would become the first Australian to coach England's men's team in their 138-year history.
Jason Gillespie was tipped to takeover as coach from Peter Moores.
Kyle Jarvis, the former Zimbabwe fast bowler, shocked many followers of the game when he announced his retirement from international cricket in April 2013.
The newly appointed England vice-captain, Joe Root could have been forgiven for playing down Moores' role in his development.
Andrew Strauss believes it was a tough decision to sack Peter Moores.
A video of former captain Andrew Strauss talking about the decisions he has taken as the Director of Cricket, England.
Kevin Pietersen hit his first county championship century in almost two years on Monday to boost his hopes of an England recall.