None of the 24 state governors elected under the platform of the governing All Progressives Congress (APC)
The governors are part of the council as coordinators for their own states.
The council was inaugurated Monday by Mr Buhari at the International Conference Centre, Abuja.
The meeting is held at the conference hall of State House Presidential Villa Abuja.
It was attended by almost all the other members of the council and is co-chaired by former Lagos state governor, Bola Tinubu.
It is not clear why the governors were absent at the event, but President Buhari recently told Nigerian voters not to re-elect any governor who failed to pay workers salaries after receiving bailout funds from the federal government.
Mr Buhari had while inaugurating the council announced that Mr Tinubu will take full charge of his re-election campaign.
However, it was gathered that Mr Buhari will be attending campaign rallies in Kaduna, Bauchi and Gombe states over the weekend.
A source at the presidential villa said Mr Buhari will travel to Kaduna tomorrow, Bauchi on Saturday and Gombe on Sunday.