If approved, the plans will replace rules under which presidential elections would have been held by postal vote only amid a coronavirus epidemic.
State news agency PAP reported that, under a new bill put forward by deputies from the governing Law and Justice (PiS) party, voters who aim to cast a postal ballot would have to notify officials 12 days before election day.
The deadline for people in quarantine amid the COVID-19 outbreak would be five days before the election.
The presidential ballot had been scheduled for Sunday but failed to go ahead amid the coronavirus pandemic, which has claimed 811 lives in Poland.
Parliamentary Speaker Elżbieta Witek is expected to announce the date of a new election within two weeks.
Law and Justice had wanted the ballot to go ahead this month, arguing that a postal ballot would keep voters safe, despite the coronavirus.
But Jarosław Gowin, the head of a grouping that is a junior partner in the governing coalition, came out against the idea, sparking a row among the country's ruling conservatives.
His staunch opposition raised the prospect that the ruling coalition partners would not be able to muster enough votes to secure parliamentary approval for a mail-in presidential ballot.
Amid the uncertainty, the prime minister's chief of staff warned last week that Poland might need to dissolve parliament and hold an early election to the legislature.
Gowin and Jarosław Kaczyński, head of the Law and Justice party, then issued a declaration which signalled they had reached a compromise.
They said that, instead of May 10, Poland’s presidential elections would be held at a later date by postal ballot.