The survey, carried out by pollsters Aximage for newspapers Jornal de Noticias, Diario de Noticias and radio station TSF, gave the current premier Antonio Costa's PS party a 38.1% share of the vote, up from 35.4% last month.
It still leaves PS short of a majority, which under the proportional representation system, equates to between 42% and 45% of the vote.
The poll put the Social Democrats (PSD), led by Rui Rio, at 28.5%, down from 33.2% in December. PS and PSD are now separated by around 10 percentage points, according to the survey.
In October, Costa's two former allies - the Communists and the Left Bloc - sided with right-wing parties to reject the minority government's budget bill, triggering the snap election set for Jan.30.
If PS fails to win a majority they will need the support of one or more parties to pass legislation.
The Left Bloc and the Communists saw support at 7.4% and 4.8% respectively in the Aximage poll.
In a debate last week, Costa said an alliance between the three was no longer possible but signalled he might seek support from the People-Animals-Nature party. Aximage's poll gave them 2.1% of the vote.
Analysts say the election alone might not solve the political impasse as no party or workable alliance is likely to achieve a stable majority.
According to the poll, which surveyed 807 people on Jan. 6 to Jan. 12 with a margin of error of 3.45%, far-right party Chega would become the country's third largest party, polling at 9%, up from 6.2% in December.
(Reporting by Catarina Demony; Editing by Angus MacSwan)
