Trump was speaking at a joint press conference on Tuesday with his Polish counterpart, Andrzej Duda - who had come to White House to press his government's arguments for a base - which he jokily suggested could be called "Fort Trump".
"If they're willing to do that, it's something we will certainly talk about", Trump added.
Warsaw could offer up to $2 billion in funding for a USA military base, according to a Polish Defense Ministry proposal reported by Polish media.
Trump also said the United States was considering a visa waiver program for Poland.
'I said I would very much like for us to set up a permanent American bases in Poland, which we would call Fort Trump, and I firmly believe that this is possible.
"I firmly believe that this is possible", Duda said, saying it would be both in U.S. and Polish interests. We want to buy more equipment.
'We are implementing the largest military investment so far as the Polish armed forces are concerned over the past 30 years, ' Duda said.
Asked if he agreed, Trump said, "I am with the president". Duda credited Trump for making Warsaw the first stop on the USA president's inaugural European trip past year and said Trump's speech was a "very important moment" for the relationship between the two countries.
Poland has been pressing for the 3,000 USA troops now deployed in Poland on a rotating basis to be upgraded to a larger, permanent presence as it faces Russia's increased military activity in the region. US soldiers are now present on its soil through NATO's back-to-back rotation.
The two are expected to discuss trade, the military and security, according to the White House. Trump said it was "ridiculous" because it benefited Russian Federation and was bad for the German people.