Venkatesh Prasad and Manoj Prabhakar are also among those shortlisted.
Ramesh Powar's previous stint as coach ended after the Women's World T20 tournament.
The women's team head coach post fell vacant when interim coach Ramesh Powar's term ended.
Gary Kirsten was India's coach they won the ICC World Cup in 2011.
Gary Kirsten was coach of the MS Dhoni-led Indian team that lifted the 2011 ICC World Cup.
Gary Kirsten was at the helm of the Indian team when Virat Kohli first made his mark.
MS Dhoni, Gary Kirsten Were Reluctant To Include Virat Kohli In Team India, Recalls Dilip Vengsarkar
Former India Skipper Dilip Vengsarkar Revealed how his tenure as India's chief selector came to an abrupt halt after just two years into his term.
While former New Zealand spinner Daniel Vettori will continue to be the head coach, the franchise has realigned the roles of Trent Woodhill and Andrew McDonald.
Gary Kirsten was coach of Team India when they lifted the ICC World Cup in 2011.
The Indian team coach is a trending topic of world cricket.
Ashish Nehra feels that he shouldn't have turned down Gary Kirsten's offer to play Test cricket for India when he was just 30 years old.
India cricket will profit from its huge talent pool, feels former head coach Gary Kirsten. The former South African Test batsman says Virat Kohli is an exciting cricketer with great attitude
Gary Kirsten feels Virat Kohli's leadership at the Test level has worked really well for the Indian team
Anil Kumble has played under foreign coaches during his long international career. He was also part of a high-profile coaching staff attached with IPL team Mumbai Indians.
The Board of Control for Cricket in India (BCCI) last week advertised for the post of head coach and set June 10 as the deadline for receiving applications
Gary Kirsten, who led India to 2011 ICC World Cup triumph, was appointed head coach of Delhi Daredevils in 2014.
Would Critics Slam Sachin Tendulkar The Way they have bashed Mahendra Singh Dhoni? Asks Gary Kirsten
Former India coach Gary Kirsten has questioned Mahendra Singh Dhoni bashers for jumping into conclusions and questioning his role in the team. The former South African opener also revealed that he is "open" for a second stint as Team India coach.
Delhi Daredevils coach Gary Kirsten says though he enjoys the "fantastic" Indian Premier League but the intensity of the tournament leaves him more stretched out.
