Hector Cuper has left his role after failing to pick up a point in the World Cup group stage and the Egyptian Football Association (EFA) was reportedly considering Queiroz as a new head coach.
Cuper's team finished bottom of Group A and was the first in the tournament to be eliminated.
The North African nation lost to Uruguay, Russia and then Saudi Arabia.
The Egyptian state media reported that Queiroz has rejected their request.
Queiroz has yet to agree to extend his stay as Team Melli coach despite claims by the president of the country's football federation that the Portuguese would lead the team at January's Asian Cup finals.
Morocco coach Herve Renard and Australia coach Bert van Marwijk are also on EFAs radar.
# Tags
