Former Australian speedster Jason Gillespie feels that the personality-clash between India coach Anil Kumble and skipper Virat Kohli was the reason behind the former putting in his papers.

"Kohli is a big personality, there's no doubt about that," Gillespie told cricket.com.au on Wednesday.

"He's a fine player and done some fine things as captain and it appears from the outside there's a bit of a clash of personalities.

"If that's the case, then everyone shakes hands and moves on. If it's not working, it's not working," the 42-year-old said.

Kumble on Tuesday stepped down from his post as India head coach conceding that a fallout with Kohli was the reason behind his decision. 

The former India captain and leg-spin legend claimed that their partnership had become "untenable" despite attempts to resolve the misunderstandings.

"It needs to be a strong relationship, that's for sure, they need to be on the same page," Gillespie said on the importance of a coach-captain relationship. 

"You don't want a ‘yes man' one way or the other. Part of a good relationship between the captain and the coach is good discussion and good debate — they certainly don't need to agree on everything.

"The overriding thing I would say is that if the captain and the coach have a shared vision, an overall goal, then how they get there is going to vary from situation to situation. 

"You don't expect the captain and coach to agree on absolutely everything but if they've got a shared vision they'll work through any potential (difficult) situations even if they might not see eye to eye," he added. 

Gillespie, who took 259 wickets in 71 Tests and 142 wickets in 97 One-day Internationals (ODI), said Kumble might have pulled the plug on his job after finding out that the discussions with the captain weren't working out.

"Kumble has decided not to (return) in the job so he must feel that those discussions and debate about what's best for the team isn't working in the current environment.

"That's probably the way Anil Kumble is looking at it. I read his statement and he basically said he likes to have good discussions about the betterment of the Indian side and he doesn't feel that's working, so he's dusted himself off, shaken hands and walked away with his head held high. That's part and parcel of professional sport."

A veteran of 132 Tests, Kumble is India's highest Test wicket-taker. As coach, he won 12 of 17 Tests and never lost a Test series at the helm.

In the shorter format, Kumble coached India to the final of the just-concluded ICC Champions Trophy, where the men-in-blue were outplayed by arch-rivals Pakistan.

In Kumble's absence, MV Sridhar was handed the responsibility to supervise the India side during the limited-overs tour of the West Indies.

The three-member Cricket Advisory Committee (CAC) comprising batting legends Sachin Tendulkar, V.V.S. Laxman and Sourav Ganguly will restart their search for a full-time replacement for Kumble.