The current Constitution allows presidents to serve one five-year term, after which they must wait another five years to run for office again.
The change would "bring continuity to public policy to reconstruct a state which has collapsed," said Carlos Romero, a legislator with Morales' Movement Toward Socialism party.
But the proposal, announced late Tuesday, was immediately rejected by opposition parties.
Morales' party is favored to lead in the July 2 elections of constituent assembly members although it is not clear if it will win the two-thirds of the 255 seats needed to approve the reform, the AP reports.
Morales won a landslide election victory in December on the promise to improve life for Bolivia's vastly poor population by fighting corruption and taking more state control over the country's natural resources.
On May 1, Morales nationalized Bolivia's natural gas industry, giving foreign companies six months to negotiate new contracts or leave.
After it turned out that Deputy Prime Minister Andrei Belousov included the Fonbet betting company in the list of backbone enterprises that can count on state support, everyone started talking about these bookmakers.