The first shelter would be built in central New Delhi at South Block, a 1931 complex next to the presidential palace that houses the prime minister's office and the foreign and defence ministries, the Hindustan Times reported.
It said the second bunker would be set up within a 400-kilometre (250-mile) radius of the capital.
Potential locations in the northern states of Uttar Pradesh and Rajasthan and in the central province of Madhya Pradesh were being studied by the head of the air force, Air Chief Marshal S. Krishnaswamy, and the chief of the nuclear forces, Air Marshal Teja Mohan Asthana, the daily said.
There was no immediate official confirmation of the report.
The Hindustan Times said the decision to build the bunkers was taken September 1 at the first meeting of the Nuclear Command Authority, which agreed India needed to ensure its leadership would not be wiped out if there were a nuclear strike.
Vajpayee's government stunned the world in 1998 by carrying out nuclear tests and declaring India a nuclear power. Pakistan carried out its own tests within days.
The Nuclear Command Authority meeting was chaired by Vajpayee and attended by senior ministers to discuss management of India's nuclear program.
The authority was created January 4 to coordinate the political council under Vajpayee and the administrative work under National Security Adviser Brajesh Mishra.
India has a policy of no-first-use of nuclear weapons, saying its arsenal is meant as a deterrent, and of not exporting nuclear technology.