Fayose said Buhari has served the nation to the best of his ability and that it is more honourable for him not to seek a re-election in 2019.
Buhari will turn 75 on Sunday, December 17, 2017.
Fayose, however, urged the President to leave office after the end of his first tenure.
The Governor stated this in a statement issued on Saturday, December 15, by his Chief Press Secretary, Mr Idowu Adelusi.
He said Buhari has served the nation to the best of his ability and that it is more honourable for him not to seek a re-election in 2019.
He said, "This is to congratulate Mr President as he clocks 75. I want to thank God for his life and pray for good health in the service of our nation and that he continues to age with grace. I wish him the best. He represents us all and we owe him prayers and cooperation where necessary, just as we also need to criticise him too where necessary.
"I am not a fan of an old man and this is not personal and peculiar to President Buhari. We need an agile president come 2019.
"We need somebody that is experienced and agile. He shouldn’t contest and the decision is his and his party. But that is not going to stop me and my party from taking over from him and his party come 2019."
Although Buhari has not made public his intentions for 2019, there are strong indications that a second term is on his card.