Egyptian presidential candidate Mohamed El Baradei would be willing to drop his candidacy if the ruling military council were to ask him to form a new government.
El Baradei is a much-respected figure in Egypt and was welcomed enthusiastically when he returned to his home country in February.
Seen as a reforming liberal, he is a Nobel Peace Prize winner and former head of the International Atomic Energy Authority.
He is reported to have visited Tahrir Square on Friday. Protesters are still in the plaza which has remained relatively peaceful although there have been clashes elsewhere in Cairo.
The demonstrators were joined on Saturday by the former national football team goalkeeper Nader El-Sayed who joined in with chants against the ruling military council.
The army is hoping that the start of elections on Monday will result in less tension on the streets and a reduction of the clashes seen in recent days.
Some Egyptians believe the poll should be delayed to guarantee security and give parties more time to campaign but the military council is determined to press ahead.