The report comes after several hundred employees of its German centres went on strike after Amazon refused to bring pay in line with comparable work in the distribution sector. Walkouts were also held in May and June.
The new centres, which would have lower labour costs, would each measure around 100,000 square metres and cost from €50m to €60m the Puls Biznesu newspaper said, citing anonymous sources.
Regional development agency official Ewa Kaucz in the western city of Wroclaw told the daily that talks were ongoing but no final decision had been made.
According to the daily, two centres could open near Wroclaw, with another in the western city of Poznan, for a total Polish workforce of 6,000 people. A first centre could open next year aimed at serving Western Europe, it said.
Two others could open in the Czech Republic. An earlier report by the Czech business daily Hospodarske noviny said Amazon was mulling a centre near the Prague airport.
Amazon employs 9,000 people in Germany at eight logistics centres, two customer service centres and at the German headquarters in the southern city of Munich.