The East African country's existing constitution bars anyone over 75 from standing as a presidential candidate. Museveni, 73, is already one of Africa's longest-serving rulers and has been in charge for more than three decades. The next elections are due in 2021.
Oil-rich Uganda is a staunch Western ally and receives substantial aid and support for its security forces, partly for sending troops to Somalia as part of an African Union peacekeeping mission.
When he first came to power, Museveni was lauded for helping restore stability after two murderous dictators known to use torture and extrajudicial executions widely, and for directing the suppression of a brutal insurgency known for mutilating civilians and kidnapping children.
But over the years, criticism has mounted over the suppression of the political opposition, widespread corruption and a poor human rights record.
Simeo Nsubuga, a legislator from Museveni's ruling National Resistance Movement (NRM) party, told Reuters the move to amend the constitution was agreed in a special meeting of the party's House members.
"We agreed that a private member should come up with a constitutional amendment bill to remove the age limit," Nsubuga said, adding the bill would be introduced on the floor next week.