He dumped the Peoples Democratic Party (PDP) for Buhari's party, the All Progressives Congress (APC), in 2020.
His Tuesday declaration follows closely on the heels of a similar one by the APC's national leader, Bola Tinubu, who also met with the president on Monday, January 10.
The two will battle for the APC ticket alongside others that are expected to officially declare in the coming weeks, including Kogi State governor, Yahaya Bello.
Vice President Yemi Osinbajo has also been rumoured to be considering a run, but he's likely to shelve his ambition due to his close links with Tinubu, a former Lagos State governor.
The president to succeed Buhari is expected to be a southerner, based on an unwritten agreement to rotate power of the Federal Government between the south and the north.
Fidelity to the agreement has become a hot topic of debate, by aspirants like Governor Bello; and the APC and PDP are yet to officially decide where to zone their tickets.