Cabinet
The US president-elect also nominated Avril Haines to serve as the director of national intelligence. She would be the first woman to do so if confirmed.
The bill will be introduced in the Budget session of Parliament which begins on Monday.
Doval was appointed as the NSA in May 2014 in the rank of Minister of State.
While Shah won Lok Sabha polls from Gandhinagar with a massive margin, Jaishankar is expected to reach Parliament through the Rajya Sabha route.
The new Council of Ministers has representation from almost all the states, except Andhra Pradesh and the north-eastern states of Nagaland, Manipur, Mizoram, Sikkim and Tripura.