Flower led England to the number-one Test ranking, three Ashes victories and the 2010 ICC World Twenty20 crown, but the former Zimbabwe batsman stood down following a 5-0 Test hammering and a fractious tour of Australia in 2013-14.
The ECB (England and Wales Cricket Board) ultimately went back to Flower's predecessor Peter Moores, who oversaw a mixed domestic summer where a new-look England team followed Test series defeat to Sri Lanka with a comeback win over India, while largely coming up short in the limited-overs formats.
Bayliss is something of a specialist in the shorter forms, holding coaching posts with New South Wales, Big Bash League team Sydney Sixers and Kolkata Knight Riders in the Indian Premier League.
The 51-year-old stepped in to coach his national team to a T20 series victory over South Africa this week owing to the quick turnaround from Australia's Tests against Pakistan in the United Arab Emirates.
Yet Bayliss might have ended up in charge of his country's old rivals after talks with ECB managing director Paul Downton, although he maintains he neither sought or was offered the post.
"They let me know half their thinking was they wanted a local Englishman," Bayliss told ESPNcricinfo.
"I was up front with them as well, I wasn't chasing it, they were the ones ringing me - I was quite happy doing what I'm doing.
"I was happy, if they wanted to take it further it was up to them. But I had no hard feelings over not getting it."
Kevin Pietersen featured in the conversations, with Bayliss told that he or any other prospective coach would not be allowed to select the star batsman following the ECB's controversial decision to release him from his central contract.
Bayliss did not seek further information on the ructions behind the scenes with Pietersen - the player's version of events having been recently aired in a much-publicised autobiography.
"All that was said was that he wouldn't be playing, and that's what it was left at," Bayliss said. "I didn't press it any further. At that stage of the negotiations it wasn't really an issue.
"To have such a player in the team would be an advantage, but you've got to go back and see how they actually got there and could that have been handled better?"
He added: "I don't know as I wasn't closely involved. It's disappointing that such a good player is no longer playing. Coaches have to coach everyone in the team. It's not just about four or five guys, there's 11 individuals in the team and you've got to try to find a way with all of them. But what went on behind the scenes with England I don't know."