The Press TV correspondent said that Amirabdollahian, Prince Mohammed and Saudi Foreign Minister Prince Faisal bin Farhan were meeting behind closed doors.
"The meeting... is a great sign of ties between Iran and Saudi Arabia warming and expanding," the correspondent, Gisoo Misha Ahmadi, said from Jeddah.
There was no immediate report about the meeting on Saudi media.
Saudi Arabia and Iran are making progress on mending ties