Although communism collapsed in Poland in 1989, some Poles still see the building as a symbol of Soviet domination, this despite its "Big Ben" make-over with the addition of a huge clock in 2000.
Poland's Deputy Prime Minister Mateusz Morawiecki said Wednesday that he "supports the idea of removing this vestige of communist domination from the centre of Warsaw.
"I've been dreaming about it for 40 years," said the 49-year-old former banker, whose father was a radical anti-communist dissident.
Morawiecki, who is also Poland's finance minister, made the comments as his rightwing Law and Justice (PiS) government marks two years in power, a period rocked by its controversial justice reforms.
Critics both at home and abroad insist they violate the rule of law, but PiS leaders insist they are only tackling corruption and removing the last vestiges of communism from the administration of justice.
Piotr Glinski, Poland's deputy prime minister in charge of culture, said this week that he had "nothing against" dismantling the tower, similar to soaring Stalinist-era buildings in the Russian capital Moscow.
Stalin regarded the 42-storey palace as his "gift" to Poles.
It was built on ruins in the heart of the Polish capital, virtually destroyed by Nazi Germany during World War II.
To this day, it houses museums, theatres, cinemas as well as a pool and offices for an array of institutions.
Disparaged for looking like huge a totalitarian-style wedding cake, an over-sized rocket or a UFO, it is said Stalin built it and others to match the skyscrapers of the Manhattan skyline.
Its detractors have come up with several exotic ideas to revamp the palace, including turning it into a tropical park with palm trees and exotic animals or repaint it pink or in the colours of the rainbow.
Warsaw residents have slowly warmed to it, with the city designating it as a protected historic monument in 2007.