Besides President Kaczynski, the plane crash near Smolensk in western Russia on April 10 killed a number of high-profile officials, including Jerzy Szmajdzinski, the leader of the Democratic Left Alliance party.
His party and the late president's Law and Justice party have yet to name new candidates. To win the election, a candidate must receive 50 per cent of votes, or it goes to a second round.
The post of president in Poland is seen more as a ceremonial role, albeit with the power to veto legislation and acting as commander in chief of the country's armed forces.
Elections were originally scheduled for later in the year, but were advanced following Kaczynski's death.
Opinion polls showed that the parliamentary speaker's main competition in the race could come from the Law and Justice party if the late president's twin brother agrees to run.
Jaroslaw Kaczynski, a former prime minister and head of the party, is expected to decide by the weekend if he would be join the electoral race.