"President Abdel Fattah al-Sissi has given his permission for Egypt to put itself forward as host for the 2036 Olympics," Minister Sobhi said.
If successful with its bid, Egypt would become the first African or Arab nation to host the Olympics.
"Egypt has solid sporting infrastructures and if it can host the Olympic Games, it will be historic," Bach said during a joint press conference with Sobhi.
An Egyptian official announced earlier in the month that Egypt, Greece and Saudi Arabia were in talks to jointly host the 2030 World Cup.
Egypt staged the 2019 Africa Cup of Nations, as well as last year's handball world championship during the Covid-19 pandemic.