The senior selection committee, led by former stumper MSK Prasad, started an extensive process to pick the support staff.
Singh, a former Mumbai Indians coach, appeared before the three-member panel, which also comprises Anshuman Gaikwad and Shantha Rangaswamy.
Under Shastri's tenure, India recorded their first-ever Test series win in Australia in 2019 after having lost on tours to South Africa and England in 2018.
Rajput is currently the coach of Zimbabwe team but has shown his interest in the India job after the ICC has suspended Zimbabwe Cricket for government interference.
Hardik Pandya played a crucial knock in the first ODI against Australia in Chennai, which eventually helped India to win.
Express takes a quick look at the credentials of those who have applied for the top job.