His father did not address the issue in his opening speech on Saturday.
But in an apparent attempt to deny any split between old and young, Hosni Mubarak praised the party's young leadership and an ambitious reform programme spearheaded by his son.
"The party's young members ... have a clear vision for the nation's future, and propose new ideas to deal with the reality,'' the elder Mubarak said.
Several alternative candidates have been floated by opposition parties and the media in the past month, including Amr Moussa, the Arab League chief, and Mohamed ElBaradei, the Egyptian head of the United Nations nuclear watchdog agency.
Egypt, a major ally of the US and recipient of billions annually in American aid, has been ruled by Mubarak for 28 years.
Presidential elections are scheduled for 2011, but Mubarak, 81, has not yet said if he will run for another six-year term.
Opposition groups earlier this month launched a campaign to revive efforts, including possible street protests, against a father-son succession.
The National Party's secretary-general earlier ruled out any decision at the convention, saying selection of a presidential candidate could only occur at a special party meeting.
Safwat el-Sherif's comments were made to a television programme and reported by the official news agency MENA.
"We have a special conference to choose the party's candidate in which the name would be put forward to the special conference, which is not held annually, and choosing the party's candidate for the presidency would be its one and only subject," he said.
This was based on the party's rules, el-Sherif said.
Opponents say Gamal Mubarak is increasingly involved in designing policy, travelling around Egypt campaigning for support and posting supporters in political posts.
Security agencies quashed protests four years ago against constitutional amendments seen as paving the way for the son.