A senior BCCI official confirmed to PTI that Shastri has submitted his application ahead of the July 9 deadline.
The interviews will be conducted the following day by the Cricket Advisory Committee (CAC) comprising Sourav Ganguly, VVS Laxman and Sachin Tendulkar.
Another notable application was that of former West Indies opener Phil Simmons, who has also coached the Caribbean team apart from Ireland and Afghanistan (as a consultant).
"Yes, Ravi has applied and so has Phil Simmons," a BCCI official confirmed the development to PTI.
Shastri, who has served as Indian team director from August 2014 to June 2016, shares a healthy rapport with the players including captain Virat Kohli.
It remains to be seen how the CAC will consider Shastri's case considering Ganguly backed Kumble over the former India all-rounder when the coach was picked last year.
Irrespective of who gets the job, it will be big shoes to fill in considering the team did well under Kumble, winning the Test series against the West Indies, Australia, England, New Zealand and Bangladesh before reaching the Champions Trophy final last month.
During Shastri's tenure, India won limited overs away series against England in 2014, reached the semi-finals of the World Cup and World T20 (2015 and 2016 respectively), won away Test series against Sri Lanka, home series against South Africa and T20 away series against Australia.
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