He has declined to speak to the media on his decision.
But on his Facebook page on Wednesday, the northern politician thanked Buhari for the appointment, but he said he could not accept it because his hands were full.
“Regarding the published nomination for an ambassadorial posting, I have not spoken to the press and may not do so anytime soon,” he wrote.
“I thank those who think me fit for the job, but I have so much in my hands already, especially the Arewa Research and Development Project (ARDP), which is the only broad platform in the north driving development.
“I have weighed the options and have decided to remain home and continue the struggle for development and good governance.”
Pauline Tallen, former deputy governor of Plateau state, had also rejected her ambassadorial appointment, citing lack of “proper consultation” as the reason for her decision.
On Monday, governors elected on the All Progressives Congress (APC) platform met with Buhari to express their concerns over the list of ambassadorial nominees.
But the president told them to put their concerns in writing.
Akintunde Akinwande, a professor at the Massachusetts Institute of Technology, has also turned down his appointment as the chairman of the Nigeria Electricity Regulatory Commission (NERC).