Brendon McCullum became England Test coach last year.
The England men's team setup underwent a significant revamp after a humiliating 0-4 Ashes series loss Down Under, with McCullum and Matthew Mott replacing Chris Silverwood as the Test and white-ball coaches, respectively.
Additionally, Test captain Joe Root resigned from the position, and batting coach Graham Thorpe and managing director Ashley Giles all lost their jobs.
Ponting said he was approached by Rob Key, who was then appointed as the English Cricket Board's new director of men's cricket.
"I got asked before Brendon took the job – there you go, you guys might be the first to find that out. I did take some calls from Robert Key as soon as he took over that job," Ponting told the Guerilla Cricket podcast.
However, Ponting, who is the head coach of Indian Premier League side Delhi Capitals, turned down the offer, as he wants to spend time with his family.
"But I'm just not ready for a full-time international coaching job, where I am at in my life. Having traveled as much as I have, with young kids now, I just don't want to be away as much as I was. And even talking to Brendon, his family is only just arriving today. When you have got kids that are in school, moving them around, that's not what I want to do," the former Australian batter said.
England has embraced an aggressive and fearless kind of cricket known as "Bazball," which was named by an English cricket journalist after the previous Black Caps skipper's nickname "Baz," under the leadership of new Test captain Ben Stokes and coach McCullum.
Since the duo took over, the England Test side has been revitalized and is yet to lose a single series.
(PTI inputs)