FILE PHOTO: Former Brazilian President Luiz Inacio Lula da Silva arrives at Federal Justice.

Luiz Inacio Lula da Silva remains far ahead in a poll out Sunday of candidates in Brazil's October presidential election, even though he has been in prison for two months.

Thirty percent of Brazilians would vote for Lula, who was  president from 2003-2010, according to Datafolha pollsters.

Lula, incarcerated at the federal police headquarters in the southern city of Curitiba since April 7, is serving a 12-year sentence for taking an apartment as a bribe.

The 72 year-old leftist politician insists on his innocence, saying the case is politically motivated.

The previous Datafolha survey, published just after Lula was imprisoned, gave him 31% support.

Datafolha said that 21% of those polled had no preference for president, while 17% would support far right-wing candidate Jair Bolsonaro and 10% ex-environment minister Marina Silva.

Lula on Friday received full support from his Worker's Party (PT), which stated in a letter that they continued to support him as their presidential candidate "to the final consequences".

Lula's time in office included a commodities-fuelled economic boom and major programs that lifted millions of Brazilians from extreme poverty.

Datafolha interviewed 2,824 voters across the country, and the poll has a two percentage point margin of error.