"President Mubarak is expected to announce his candidacy tomorrow while visiting the Munufiya governorate," the party official said on condition of anonymity on Wednesday.
Mubarak, 77, originally hails from a small town in that governorate.
"President Hosni Mubarak will announce tomorrow his decision to run for the presidency," the government-owned Al-Akhbar daily also reported.
"As soon as he announces his candidacy, the National Democratic Party's policy committee will review the candidacy and take a vote," the newspaper added.
The NDP's policy committee is led by Mubarak's son Gamal.
Mubarak has been in power since the 1981 assassination of Anwar Sadat.
The September poll will be the first contested presidential election in Egypt.
Until now Egyptians had only been able to say yes or no to a single candidate appointed by the NDP-dominated parliament.
The constitutional change allowing for multi-party elections was approved in a May referendum, although the country's judges have said the official results of the vote were rigged.
The opposition has claimed that the changes make it impossible to mount a serious challenge to Mubarak, and many opposition figures and parties who had initially voiced their intention to run have decided to boycott the vote.