Sources have told NDTV that it was now a "two-horse race" between Shastri and Sehwag.
A total of six contestants had been shortlisted for interviews by the Cricket Advisory Committee. Among the others who have applied are Lalchand Rajput, Tom Moody, Richard Pybus and West Indian Phil Simmons.
The coaching issue snowballed after Anil Kumble quit the post shortly after the ICC Champions Trophy, where India lost to Pakistan in the final.
He had tweeted his resignation, stating that his relationship with India captain Virat Kohli was 'untenable'.
Shastri was not among the applicants in the first lot and put in his candidacy only after the Board of Control for Cricket in India (BCCI) reopened the application process.