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The outgoing coach said sharing the leadership burden isn't a bad idea in a post COVID-19 world.
Ravi Shastri said the former BCCI president had had "more faith" in his coaching abilities than he himself.
The former captain will replace Ravi Shastri, whose term gets over after the ongoing ICC T20 World Cup.
Speculation is also rife that he might take up a coaching role in the IPL.
Earlier, spinners Ravindra Jadeja and R Ashwin helped India restrict Namibia to 132/8.
Dravid's trusted lieutenant Paras Mhambrey is expected to be the bowling coach while Vikram Rathour is likely to continue as batting coach.
Shastri's contract as India's head coach is set to end after the T20 World Cup and the 59-year-old has already confirmed that he won't be seeking an extension.
The star batsman will continue to lead India's test and one-day teams.
Kumble was the coach of the Indian team for a year between 2016 and 17 before a bitter fall-out with captain Kohli led to him tendering his resignation.
Shastri said that he was getting flak for no fault of his.
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