Sisi, 59, intends to make the announcement on or before the January 25 anniversary of the revolution in order to prevent any unexpected violence by Morsi's supporters, Asharq al-Awsat newspaper quoted sources as saying.
In his speech, Sisi will explain that he is running in response to popular pressure, they said.
The sources said they have asked Sisi to announce his candidacy for presidency in the next couple days to reassure Egyptians.
In remarks to the Saudi daily Okaz, Amr Moussa, who was a former candidate in the 2012 presidential election and head of the 50-member Constitutional Committee, described Sisi as "the most popular figure in Egypt today."
"He will be the front runner in the race to win the presidential election. He has a great chance of winning this election," he said.
The Supreme Electoral Committee (SEC) yesterday announced that the newly drafted national charter was approved by 98.1 per cent of voters, according to state-run media.
The new charter would replace the one approved under Morsi, who was toppled by the military in July following mass protests demanding his ouster.
Morsi's Muslim Brotherhood had called for anti-government protests and boycotted the referendum, seeing it as part of a coup against the freely-elected leader.
The new charter, drafted by a liberal-dominated committee appointed by the government, would ban political parties based on religion, give women equal rights and protect the status of minority Christians.
