Despite this lead, the Socialists still fall short of the absolute majority they won in the last general election in 2005 when they captured 45 percent of the vote and 121-seats in the 230-seat assembly.
The last Marktest poll published on September 12 gave the Socialists 36.7 percent of the vote against 32.4 percent for the PSD.
The gains by the Socialists ahead of Sunday's election came mostly at the expense of the far-left Left Block which saw support fall from 16.2 to 9.0 percent.
The right-wing Popular Party would capture 8.2 percent of the vote while the Communists would get 7.2 percent, according to the poll published Thursday.
The poll of 806 eligible voters was carried out between September 18 and 21. It has a margin of error of 3.45 percent.
The Socialists suffered a shock defeat in the European Parliament elections in June.
"The most likely scenario after the elections is that of a minority socialist government that negotiates parliamentary agreements on a case by case basis," University of Lisbon political science professor Antonio Costa Pinto told AFP.
Most analysts rule out a central bloc government with the participation of the two main parties because of the bitter campaign and the vast policy differences between the Socialists and the PSD, who have been split between populists and traditionalists since the last election.
The Socialists favour major public works projects, like the construction of a new airport in Lisbon and a high-speed rail network, to revive the struggling economy. The PSD vehemently argues that the country can not afford such projects.
In a heated television debate with the prime minister, Ferreira Leite said "a political understanding with Socrates is out of the question", adding she would not mind forming a minority government if the PSD wins the election.
She has accused the government of stifling opposition opinion with a climate of "democratic asphyxiation".
Socrates has avoided commenting on any post-election coalitions.
"The choice is between the Socialists and the right, between me and Manuela Ferreira Leite," he said at a campaign rally.
Throughout the campaign Socrates, the first Socialist leader to have won an absolute majority in parliament since the end of a lengthy right wing dictatorship in 1974, has targeted the left-wing voters his party lost in the European polls.
The party platform includes a promise to legalise gay marriage in what was seen as an effort to cut the appeal of the far-left Left Block which is forecast to almost double its vote to more than 10 percent.
Socrates has also vowed to make job creation the top priority. The number of jobless recently passed half a million and he has had to defend his painful structural reforms and budgetary rigour, which he argues have allowed Portugal "to better resist" the global economic downturn.
Portugal posted gross domestic product growth of 0.3 percent in the second quarter of the year, making it one of the first nations in Europe, along with Germany and France, to show signs of emerging from recession.
The Left Block, a coalition of small Trotskyite, Maoist and other far-left movements, and the Communists have ruled out taking part in a government led by Socrates, who they have accused of adopting right-wing economic policies.
"Whoever is the winner of the election, there is a real risk of ungovernability after, especially when it comes time to vote on the budget," said Costa Pinto.
In a presidential election in 2006, PSD candidate Anibal Cavaco Silva, exploiting splits in the left, became Portugal's first right-wing head of state since the dictatorship ended.
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