Former India captain Shastri has been appointed team director for his country's upcoming one-day international series against England, with Fletcher working under the legendary former batsman as head coach.
Shastri's appointment for the five-match ODI series, which begins in Bristol next Monday, raised questions about Fletcher's position following the tourists' 3-1 Test series defeat to Alastair Cook's side.
The Board of Control for Cricket in India (BCCI) also revealed that bowling coach Joe Dawes and fielding coach Trevor Penney will be given a rest, with Sanjay Bangar and Bharat Arun adding to the coaching staff and Ramakrishnan Sridhar taking over a fielding coach for the ODI series.
The 52-year-old Shastri, though, stated on Wednesday that he has not got designs on taking Fletcher's job and has every confidence in the experienced Zimbabwean.
When asked if Fletcher's position is under threat, Shastri told Sky Sports News: "My job is for the moment and I will not be interested in Duncan Fletcher's job.
"Let me make it loud and clear, Duncan Fletcher will remain coach of the Indian team.
"He remains the head coach firmly, he'll have two assistants from India who will work under him and with him and I will work with him from the top."
Shastri has stressed the importance of lifting the spirits of the India team following their dismal performances in the last three Tests after winning at Lord's.
He said: "We've got to try and get the morale and confidence going so the boys start to enjoy themselves.
"I don't think there's any need to panic, for India is a young side in transition."