Najib's session will be aired at 10pm on Monday while Dr Mahathir will appear at the same time on Thursday.
Their appearances are part of a series of live interviews lined up, focusing on the future of Malaysia and the region as a whole.
Viewers can call the live show at +12022752360, or email their questions to email@example.com.
Live TV interviews with Najib and Dr Mahathir next week
New Straits Times, Malaysia