From the GACA website, they do the new Saudi medical, but I believe they also do FAA:
http://www.gaca.gov.sa/avmed/avmeddir.htm
Dr. Khalid A. Gharib
Jeddah
02-686-4397
02-686-4626
02-686-1671
0503677546
Dr. Mohammed Hani Younis
Jeddah
02-686-4397
02-686-4626
02-686-4233
0503662449
Dr. Salim Ahmed Al-Sayed
Jeddah
02-686-4397
02-686-4626
02-686-4584
Dr. Mohammed A. Monem
Jeddah
02-682-0022
Ext. 659/497
0505604391
Dr. Mousaed Z. Adi
Jeddah
02-685-4036
02-685-4037
0555675690
Dr. Ahmed Mumtaz Jad
Riyadh
01-4616777
0505192616
Dr. Amal Samy
Riyadh
01-4645050
01-4650840
01-4650828
0509279160
Dr. Mohamed Sherief Al-Toukhi
Al-Khobar
03-8143333
Ext. 3205/3100/3200
0500664753