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.