Already, two key ministries -- Defence and Environment -- are without a full-time minister.
Finance Minister Arun Jaitley and Science and Technology Minister Harsh Vardhan are holding the additional charge of these two portfolios respectively.
Mr Naidu, whose candidature as the NDA's vice presidential candidate was announced today, currently holds charge of the ministries of Information and Broadcasting and Urban Development.
BJP sources said a reshuffle in the Union council of ministers is expected after the monsoon session of Parliament, and some new faces could also be inducted into the Cabinet.
Prime Minister Narendra Modi first expanded his cabinet in November 2014 when he inducted 21 new faces, including Mr Parrikar as Defence minister.
In July last year, PM Modi undertook another reshuffle in which he appointed Prakash Javadekar as the Human Resource Development minister, replacing Smriti Irani, who was shifted to textiles.