A poll by private opinion research firm Cedatos showed the consitutional changes, put forward by Ecuador's Constitutional Assembly in July, was expected to be approved by more than 60 per cent of Ecuadorians.
More than 24 per cent were expected to vote against it and the government believes the winning margin will be 70 per cent.
The constitutional changes have been made by leftist majorities in power in Ecuador, in line with those that have been made in Venezuela and Bolivia, repudiating the neoliberal policies of the 1990s.
Ecuador's changes, however, fall short of nationalising the country's national resources as Bolivia and Venezuela have done.
The consitution's 444 new articles to expand the president's powers are said to be necessary to end political instability in a country that, in the last 10 years, has removed three presidents from office before their terms were finished.
Branded as "hyperpresidentialist" by the conservative opposition, the new constitution would allow the president to run for two consecutive, four-year terms, dissolve congress and call early elections.
Correa, 45, has already announced his intention to run for re-election in February 2009, if it is approved, in which case early elections would be convened by the Constitutional Assembly.
Jaime Nebot, the leader of the opposition Social Christian party and the mayor of Guayaquil, has criticised the new constitutional changes, which he says would create a centralised form of government that would threaten private property.
The government expects 70 per cent of voters will be in favour of the constitution [AFP]
"Do you think we can model ourselves after Venezuela, a country swimming in oil money, but whose people have to line up to get food?
"Or Bolivia, a country split down the middle because its government doesn't understand?" Nebot recently said.
The Roman Catholic Church, a major player in the predominantly Catholic country, has also criticised the new constitutional changes, in particular articles it says will lead to the legalisation of abortion and same-sex marriage.
Ecuador's emigrant communities, the biggest being in Spain, the United States and Italy, are also eligible to vote.
About 60,000 police and military personnel have been deployed around the country and sales of alcoholic drinks have been banned from Friday until Monday.
Correa, fearing the province of Guayaquil might become a thorn on his government's side, has asked the Organisation of American States (OAS), in charge of election monitors, to validate the final vote tally in the area.
"You have to remain very alert to the losing side's usual argument discrediting a victory ... as a fraud," Correa told OAS officials in Ecuador earlier this week.
Enrique Correa, an OAS spokesman, said that his group has so far found "no signs of fraud in the works".