The official MENA news agency reported on Thursday that Mubarak said Egypt would not follow the example of Syria, where Bashar al-Assad took over power from his father in 2000.
"This is nonsense... the regime in Egypt is republican, there is no hereditary transfer of power. This happened in a certain country (Syria), it will not happen in Egypt," he said.
Gamal Mubarak, 40, was named in 2002 to head the ruling National Democratic Party's powerful political committee, fuelling rumours he was being prepared to succeed his father.
But the 75-year-old president, who has been in power since 1981, said he was initially reluctant to let his son join the ruling party.
"The talk of a hereditary transfer of power started after my son joined the party. But he joined with great difficulty, after several requests were conveyed to me," he said.
Gamal Mubarak was tipped to
succeed his father
The issue of the succession came under renewed attention in November when the president interrupted a keynote speech to parliament because of what officials said was a bout of severe 'flu.
Mubarak has never named a vice president, the route he and his predecessor Anwar al-Sadat, took to become head of state, both after a career in the army.
The constitution says if the president dies or is unable to exercise his functions, the speaker of parliament becomes acting president for 60 days.
During this time parliament must designate a presidential candidate by two-thirds majority. The candidate must then be endorsed by referendum.