ECB director of cricket Andrew Strauss last week confirmed Gillespie was one of the candidates for the job and Gillespie said he had spoken with Strauss about the position.
But England’s The Telegraph reported the ECB have opted against appointing Gillespie, in favour of Bayliss.
Bayliss has had successful stints as coach of Sri Lanka, Sydney Sixers, NSW and Indian Premier League side Kolkata Knight Riders.
During his time as Sri Lanka coach Bayliss worked alongside current England assistant Paul Farbrace.
The appointment of an Australian to lead England would add further interest to the impending Ashes series between the two teams.
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Australia are currently in the Caribbean ahead of a Test series against the West Indies.
The first Ashes Test against England starts on July 8 in Cardiff, Wales.