Mubarak is believed to be preparing his son Gamal, now a senior party official, to be his eventual successor.
But the 43-year-old former investment banker has denied having any ambitions to inherit the presidency from his father.
Some analysts say a succession to Gamal could only happen while Mubarak is alive to prevent a power struggle or military intervention.
Making the transition to the presidency more complex, Mubarak has refused to appoint a vice-president.
The route to the presidency has come via the vice-presidency in Egypt’s two previous successions.
Al Jazeera’s Amr El Kahky says that economic reforms have ushered in a new era of privatisation in Egypt, but they have also given rise to numerous strikes and the largest spate of labour unrest in decades.
It is an issue that is high on the agenda for the NDP conference in Cairo.
The reforms are proving divisive, and could even set Mubarak against his likely successor – his own son, El Kahky says.
Mubarak’s party is now facing an intense battle between the old guard wanting to slow down and the new guard looking for more openness and power for private business.
El Kahky said: “On one side is Mubarak himself and his close ally Safwat Al-Sharif, the party secretary. He has been serving with Egypt’s rulers for more than three decades now. Power is his middle name. And he is not ready to give it up any time soon.
“On the other side is Ahmed Ezz, a successful businessman and entrepreneur. Having already managed to get rid of many old faces in the party, he now wants to give more power to private business. And he is supported by Gamal.”
Gamal Essam El-Din, a journalist with Al-Ahram weekly, told Al Jazeera: “It is a decisive point for the party. But if you ask members of the ruling party, in most cases they will deny any hint of division within the party.”
However, Mohamed Ragab, leader of the NDP majority in the parliament’s upper house, said: “Within a party as big as ours, there’s only a struggle of ideas. Discussion.”