The NPP leader said any such suggestion can only be made by one who does not understand the country's laws.
He was speaking to thousands of NPP supporters during his three day campaign tour of the Central Region.
The president, John Mahama had taken a swipe at Nana Akufo-Addo during his campaign in Suhum, describing him as a vindictive leader.
Mr Mahama, made reference to a video that had gone viral on social media in which the ex-president John Kufuor was advising NPP delegates to elect a peaceful, not a vindictive leader to lead the NPP to victory in the 2008 elections.
He concluded that the ex-president was referring to Nana Akufo-Addo and cited recent misunderstanding within the NPP that led to the suspension of three national executives of the party.
He said with the track record of the NPP leader, he would not be surprised chiefs will be destooled for criticising Nana Akufo-Addo.
But the NPP leader has hit back. He does not understand how the president, who should have been the custodian of the country's will be the one suggesting another president will destool chiefs.
Is the president ignorant of the laws of Ghana? he asked exp
laining that the constitution guarantees the independence of the chieftaincy institution and no president can destool a chief.
Nana Akufo-Addo said he will be the last person to do the things the president is suggesting because his respect for the chieftaincy institution is unrivaled.
Chronicling the history of the Chieftaincy institution within the democratic dispensation, Nana Akufo-Addo said it was his father, Edward Akufo-Addo, then Chief Justice who in the 1969 Constitutional Commission institutionalised the independence of the chieftaincy within the country's constitution and that has been the case since then.
He said th
e president has no message to the people and has rather resorted to making unfounded claims and allegations.