Bradley, Colombian Francisco Maturana and Zoran Filipovic, the former Montenegro coach, are being interviewed for the job.
Bradley was fired last month as U.S. coach after nearly five years in the job in which he led the team to the 2009 Confederations Cup final.
Maturana made his name as coach of his native Colombia at the 1990 and 1994 World Cups.
The new coach will be tasked with qualifying Egypt for the World Cup for the first time since 1990.
(Writing by Mark Gleeson in Cape Town; Editing by Ed Osmond)