Dravid's trusted lieutenant Paras Mhambrey is expected to be the bowling coach while Vikram Rathour is likely to continue as batting coach.
Shastri's contract as India's head coach is set to end after the T20 World Cup and the 59-year-old has already confirmed that he won't be seeking an extension.
Shastri said that he was getting flak for no fault of his.
"I've achieved all I wanted," Shastri said when asked whether the ICC T20 World Cup would be his last outing with Team India as head coach.
Kumble was the coach of the Indian team for a year between 2016 and 17 before a bitter fall-out with captain Kohli led to him tendering his resignation.
The star batsman will continue to lead India's test and one-day teams.
Instead of talking about the fifth Test being called off, Shastri chose to focus on the performances of the Indian team in the series.
The trio will remain in isolation for at least the next 10 days and wont' be travelling to Manchester for the final Test.
Bowling coach Bharat Arun, fielding coach R Sridhar and physiotherapist Nitin Patel are also isolating "as a precautionary measure."
The Indian skipper shares a close relationship with the head coach.