Kumble, who had an unceremonious exit as India coach after differences with Kohli, is competing with Bisheshwar Nandi (gymnastics), Balwan Singh (kabaddi), Harendra Singh (hockey) and Vijay Davecha (golf) for the award.
The nominations were announced today.
The winners will be announced at a ceremony to be held in Mumbai on November 11.
There are eight categories including sportsman of the year which has pitted cricketers Cheteshwar Pujara, R Ashwin and Hardik Pandya against each other.
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The jury is chaired by former all-England champion and chief national badminton coach Puellela Gopichand, and also comprises multiple Grand Slam winner Mahesh Bhupathi, legendary sprinter PT Usha, former world number one shooter Anjali Bhagwat and former India hockey captain Arjun Halappa.
Terming this an "authentic" sports award, Bhupathi said: "Having an award at the end of a season not only inspires youth but recognises the past players. It's exciting to have an authentic sport award in the country. I don't think we have one. It will definitely create an aspiration to achieve more."
The finalists for the sportswoman of the year award in individual sport are Olympic silver and bronze medalist duo of PV Sindhu, Sakshi Malik along with gymnast Dipa Karmakar, athlete Lalita Babar and tennis ace Sania Mirza.
For the male category in individual sport, javelin thrower Neeraj Chopra, cue sports ace Pankaj Advani, golfer SSP Chawrasia, and in-form shuttler Kidambi Srikanth are the finalists in the race for the best sportsperson of the year award.
The other categories are Emerging Sportswoman of the year
Aditi Ashok (golf), Ritu Phogat (wrestling), Smriti Mandhana (cricket); and Emerging sportsman of the year Harmanpreet Singh (hockey), Neeraj Chopra (athletics), Ramkumar Ramanathan (tennis), Sameer Verma (badminton) and Vidit Santosh Gujarathi (chess).
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