The draft law, which has been presented to the cabinet for approval, also awards him a lifetime salary.
It also proposes that Mr Nkurunziza be elevated to the title of "supreme leader" when he steps down in May.
Burundi was plunged into a constitutional crisis in 2015 when he successfully ran for a third term.
The move sparked violent protests by opposition supporters which morphed into reprisal attacks.
Last year a UN commission accused the government of human rights abuses, including executions, arbitrary arrests, torture and sexual violence.