Lula received 47 per cent voter support against Bolsonaro's 32 per cent in the latest survey by pollster Datafolha, compared to 47-29 per cent in July.
In a potential second-round runoff between the two candidates, Lula - president from 2003 to 2010 - would return to office with 54 per cent of the votes against Bolsonaro's 37 per cent, the poll suggested.
Leftist Lula has seen his advantage in the runoff shrink each month from the 29-point lead he had in December.
The Datafolha poll of 5744 Brazilians of voting age also showed 51 per cent claim they would never vote for Bolsonaro, three percentage points below last month, while Lula's rejection went up by one percentage point to 37 per cent.
Bolsonaro has attempted to lure voters in recent months by passing a major spending package that included a welfare program for poor Brazilians and measures to tackle fuel prices, which in turn has helped inflation rates begin to slow.
His approval rate went up to 30 per cent in August, from 28 per cent in July, according to the poll.Â
Meanwhile, 43 per cent of those interviewed said they disapproved of the far-right leader's government, against the 45 per cent recorded last month.
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