Shastri's name was recommended by former captains during a meeting with Indian cricket chiefs here to discuss the fallout of India's first round ouster from the World Cup in the Caribbean.
"Shastri has sought some time to reply to our proposal," an official of the Board of Control for Cricket in India (BCCI) said.
It is expected that Shastri's appointment as interim coach and manager will be ratified at the working committee meeting of the BCCI here on Saturday.
Chappell, the former Australian captain, did not extended his two-year stint as coach which ended with the World Cup, citing "family and personal reasons."
Shastri, 44, widely regarded as a shrewd thinker of the game, became a television commentator after retiring from international cricket in 1992.
A right-hand batsman and left-arm spinner, Shastri played 80 Test matches in which he scored 3,830 runs and claimed 151 wickets.
He also made 3,108 runs and took 129 wickets in 150 one-day internationals.
Shastri led India in one Test match, securing victory over the West Indies on an underprepared wicket in Chennai in 1988 where debutant Narendra Hirwani grabbed 16 wickets.
Shastri, usually a dour batsman, hit spinner Tilak Raj for six sixers in an over in a first-class match in 1985, only the second man to achieve the feat after West Indian great Garfield Sobers.
South African batsman Herschelle Gibbs became the first batsman to hit six sixers in an over in an international match during the ongoing World Cup.
India will play two Tests and three one-day internationals on the tour of Bangladesh starting on May 10.