The move is proposed in a bill put forward on Tuesday by lawmakers from Poland’s governing conservative Law and Justice party.
Opposition politicians have called for the presidential ballot, scheduled for May 10, to be postponed.
They argue that election campaigning is restricted or has been made impossible by the coronavirus outbreak in Poland.
But politicians from the ruling party have accused the opposition of playing for time in the hope that the gap will narrow between incumbent conservative President Andrzej Duda, who is bidding for a second term, and his rivals.
Opposition presidential candidates are way behind Duda in the polls, recent surveys have shown.
In a special televised address broadcast on Tuesday evening, the conservative Speaker of the lower chamber, Elżbieta Witek, appealed to the Senate, the upper house, to “proceed efficiently” with the bill that would give all citizens the right to a postal ballot.
Poland’s conservatives won a second term in power in parliamentary elections last autumn, but lost control of the Senate.
A total of 2,311 people have tested positive for the COVID-19 disease in Poland, with 33 deaths from the coronavirus so far, officials said on Tuesday evening.