Nationalist Duda, whose term in office expires in 2025, was one of Trump's preferred international partners during the Republican's presidency. The Polish president's top aide has said they remain in contact.
Tabloid Fakt and news portal WP.pl both cited sources as saying that an informal meeting would take place during a visit to New York during which Duda is scheduled to meet United Nations Secretary-General Antonio Guterres.
Poland's Presidential Palace did not immediately respond to a request for comment.
Trump, who went on trial in New York over a hush money payment on Monday, is in a tight race with U.S. President Joe Biden ahead of the November presidential election.
Many European leaders have long been nervous that another Trump presidency would mean waning U.S. support for Poland's neighbour Ukraine and the NATO military alliance.
Poland is a staunch ally of Ukraine and both Duda and liberal Prime Minister Donald Tusk have urged the United States lawmakers to approve $60 billion in military aid to Ukraine.
While Tusk and Duda are bitterly divided over a host of domestic issues, they are united on the importance of continued support for Ukraine.
Jacek Siewiera, the head of the Polish National Security Bureau, told private broadcaster TVN24 that a meeting between Duda and Trump was not on the official schedule but that it would be a mistake to rule it out.
Hungary's nationalist prime minister, Viktor Orban, met Trump in March, saying afterwards that Trump told him he would not give money to help Ukraine fight Russia if he wins the U.S. presidency again.
(Reporting by Alan Charlish, additional reporting by Anna Wlodarczak-Semczuk; Editing by Ros Russell)
