The Board of Control for Cricket in India (BCCI) said on Sunday that it had received 57 applications for the post but did not reveal any names.
Former team director Ravi Shastri, current chief selector Sandeep Patil and ex-pace bowler Venkatesh Prasad were among a few top former players who made their coaching intentions public.
But on Monday Kumble, who has mentored Indian Premier League sides such as Mumbai Indians and Royal Challengers Bangalore, was reported to have also thrown his hat in the ring.
BCCI receives 57 applications for head coach position
"Yes, I have applied," the former India skipper was quoted as saying by The Indian Express newspaper.
The 45-year-old bagged 619 Test wickets in 132 matches and is only the second bowler in cricket history after England's Jim Laker to have taken all 10 in a Test innings.
Kumble has previously served as the president of his state association in Karnataka and headed BCCI's technical committee. He is currently the chairman of the ICC cricket committee.
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However Kumble does not fit the BCCI criteria of having "coached a cricket team of any of the member countries of the ICC (International Cricket Council), at the first class or at the International level".
Overseas coaches such as Australia's Stuart Law and Dav Whatmore, who was recently sacked by Zimbabwe, are also being floated by India's media as possible applicants.
The list will now be pruned by board secretary Ajay Shirke and the appointment of the new coach is expected to be made before India's tour to the West Indies in July.
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