In an interview for public broadcaster TVP, the Polish defence minister said that talks were “advanced”.
But Błaszczak declined to name a date by which the bases could be set up.
Meanwhile, the Pentagon has been tasked with reporting on the feasibility of setting up US military bases in Poland, according to reports.
Błaszczak has previously said that permanent US army bases would provide a further security guarantee for Poland and that the country was ready to cover part of the costs involved.
Paweł Soloch, head of the Polish president’s National Security Bureau (BBN), said in June that Poland was eyeing becoming “a hub for the presence of American troops in Europe.”
Leaders from the Baltic states welcomed the idea of a permanent US military base being established in Poland, Polish Radio reported.
Amid fears of Russian aggression following Moscow’s annexation of the Crimea region of Ukraine in 2014, NATO decided at a Warsaw summit in July 2016 to deploy four rotating multinational battalions to Poland and the Baltic states.