The former Team India captain makes this revelation in his soon-to-be-published autobiography "A Century is Not Enough".
During Chappell's stint with the Indian team, Ganguly lost the captaincy and also his place in the squad for a while.
Ganguly also says he felt "angry" and "disillusioned" on being left out of the Rest of India squad for the Irani Trophy in 2008, a few months before he announced his retirement, and saw it as a clear indicator of how the selectors thought of him.
"I asked him point-blank, did he think I was no longer an automatic choice in his eleven? Kumble - the gentleman that he has always been - seemed embarrassed with my call. He told me he hadn't been consulted before the selection committee chaired by Dilip Vengsarkar took this decision," Ganguly writes in the book, co-authored by Gautam Bhattacharya and published by Juggernaut Books.
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The publishing house has posted a free preview of the first chapter of the book on its website.
Ganguly then played domestic cricket - the little-known J P Atrya Memorial Trophy in Chandigarh - to convey a strong message to the selectors.
The Indian team for the first two Test matches of the Australian series was soon announced. Ganguly found his name in it. Simultaneously a Board President's team was also announced. This was the secondary team that would take on the Australians in Chennai.
"But its mindset seemed to be no different from the previous committee's. The message was crystal clear - that a veteran of 100-plus Test matches, a certain Sourav Ganguly, was again on trial," he says.
"I felt extremely agitated. That is when I told my father that I needed to call it a day. Enough was enough. My father was a bit surprised. In the past when Greg Chappell had kept me out of the team and I was desperately fighting to claw my way back, he had wanted me to retire, unable to bear his son's struggle.
"So three years later when he heard the same person was throwing in the towel, he was surprised," he goes on to add.
Ganguly says he had a chat with Kumble who told him not to decide anything in a hurry.
"Cricketing history has recorded that I had an outstanding final series. Got a hundred in Mohali and narrowly missed the second in Nagpur," Ganguly tells about his performance.
Sharing another anecdote, he says, "In Mohali a journalist came and asked, 'Did the hundred give you special pleasure because Greg Chappell was watching it from the Australian camp?' I said, at this stage of my cricketing career it didn't matter at all. I had got past all that. For me he didn't exist any more."
"I had rejected his offer earlier in the day, but could not refuse a second time. Ironically, my captaincy career had begun exactly eight years ago on this very day. I handled the bowling changes and field placements while the last Australian wicket batted.
"But I must admit, at that stage, I found it difficult to focus. So after three overs I handed it back to Dhoni saying, it is your job, MS. We both smiled," he writes.