Speaking to a committee of lawmakers about the issue on Wednesday, President Yoweri Museveni asked: "If someone votes, why can't he be voted for?"
Lawmakers are considering the bill that would remove a clause that bars anyone over 75 from holding the presidency.
There are no presidential term limits in Uganda, and Museveni's critics say the age clause is the only measure left to block a possible life presidency for the 73-year-old.
The president last week tweeted about his health regime, saying he doesn't "have time for sickness."
Museveni, a US ally on regional security, has ruled the East African nation since taking power by force in 1986.