New England head coach Trevor Bayliss twice turned down the job, according to former Australia bowler Geoff Lawson.
Bayliss, 52, was appointed on Tuesday, but New South Wales bowling coach Lawson says his former colleague rejected the offer before Peter Moores took charge in 2014.
"He said no then, and in fact last week he also said no again," said Lawson.
Lawson said the chance to work with England assistant coach Paul Farbrace was influential in Bayliss's decision.
"Those two worked together way back in Kent days and Sri Lanka," Lawson, 57, told BBC Radio 4.
"They've got a very good working relationship and Trevor likes to have people around him he knows he can trust and knows what they can produce.
"And they (the England and Wales Cricket Board) have made him a very good offer."
Moores, who was also England head coach between 2007 and 2009, was sacked for the second time in May.
Australian Bayliss had a brief spell coaching at Kent in 2003, and was in charge of Sri Lanka from 2007 until 2011.
Before accepting the England job, he was combining coaching roles with New South Wales in Australia and Kolkata Knight Riders in the Indian Premier League.
Lawson added: "He was very happy doing his IPL job six or seven weeks a year, plus looking after New South Wales the rest of the time.
"He had a pretty full schedule. After about four years with Sri Lanka he was looking to spend a bit more time at home."
Bayliss will take charge of England in time for the start of July's Ashes series against Australia, whom he coached in Twenty20s last year.
Farbrace, stand-in coach for England's victory over New Zealand in the first Test, will remain in charge for the final Test at Headingley starting on Friday.