The governors who attended the meeting are Atiku Bagudu (Kebbi), Aminu Masari (Katsina), Abdulaziz Yari (Zamfara) and Ibikunle Amosun (Ogun).
Vice-President Yemi Osinbajo also attended the meeting that took place at Aso Rock.
On their way out, the politicians declined to speak with reporters.
But a presidential source told TheCable that the governors had met with Saraki on Wednesday night and later convinced Buhari to discuss with him.
The source said the president would hold a similar meeting with Yakubu Dogara, speaker of the house of representatives.
“Last night, some APC governors came to see the senate president as part of ways to reconcile the various groups in the APC. They were the ones who then went to tell the president that he must see Saraki,” the source said.
“Today, the senate president met with the president, the vice-president and some of the governors. Issues around the crisis in the party were deliberated on during the meeting.
“More meetings will still hold. The president will soon invite Dogara and others. The governors were mandated to continue with further meetings and brief the president.”
Saraki and Dogara belong to the new Peoples Democratic Party (nPDP) bloc of the APC. The group played a significant role in the victory of the ruling party in the 2015 elections.
The group had demanded to meet the president over some grievances but the president called their bluff and asked its leadership to meet Osinbajo.
Some nPDP members have teamed up with other aggrieved APC members to form R-APC, a faction which signed an alliance with 38 political parties, including PDP, to dislodge Buhari.
There are reports that Saraki and Dogara would leave the APC soon. Saraki and three APC governors held secret talks with PDP leaders on Wednesday.
Adams Oshiomhole, national chairman of the APC, is doing his best to resolve the crisis in the party.
He met with Samuel Ortom, governor of Benue state, on Thursday, and vowed that the governor who had earlier announced that he was considering joining a new party, would not leave APC.
Ortom was among the three APC governors who met PDP leaders on Wednesday.