Laxman is a part of the CAC that also comprises the likes of Sourav Ganguly and Sachin Tendulkar.
According to a report in India Today, the former India batsman said that the body wanted Kumble to continue as coach, but he chose to step down instead.
Laxman revealed that the incident left a bitter taste in the mouth.
'We at the CAC thought Anil should continue as coach'
"I don't think Kohli crossed the line. We at the CAC thought Anil should continue as coach but he thought the right decision was to quit and move ahead. It left a bitter taste in the mouth," said Laxman.
The legend felt that the Kohli-Kumble partnership didn't work out.
"We did a very elaborate process — unfortunately, Kohli and Kumble did not work out."
How did the saga unfold?
According to reports, the issues had surfaced between the two when Kumble used to send instructions to Kohli on the field.
There were disagreements over team selection as well.
The cricketers did not find it easy under Kumble.
The former ace spinner was a demanding coach and Kohli's team wanted someone more free thinking and relaxed.
That's where things reached a tipping point.
The partnership was untenable: Kumble on Kohli
During the ICC Champions Trophy in 2017, the saga was exposed and it got a lot of media coverage.
Kumble's decision came just 4 days ahead of the limited-overs tour of the Caribbean.
Kumble had said, "The misunderstandings between the captain and me, it was apparent that the partnership was untenable. I believe it was best for me to move on."
Here's how India performed under Kumble
Under Kumble's coaching stint, India won five successive Test series. It started with an away series win against West Indies. India then won 4 successive home Test series against New Zealand, England, Bangladesh and Australia. India won two ODI home series as well.