"If this happens, the location will be announced very soon," Trump said in a post on Truth Social.
"This will be a historic step for our Great U.S./Polish Alliance," he added.
Nawrocki later thanked Trump for his "kind words ... friendship and ... strong commitment to the Polish-US partnership."
"We are ready to continue our efforts to strengthen our defence cooperation: seriously, responsibly, and always together," he wrote on X.
"I can assure you that the Polish government will do its utmost to provide the best possible location for the US Army base," he added.
The head of Nawrocki's office, Zbigniew Bogucki, called Trump's announcement "great news for Poland," noting that it came on the 87th anniversary of the Soviet invasion of Poland in the early days of World War II and "at a time when the predatory instincts of Putin's Russia threaten the free world."
He described Nawrocki and Trump as "bold and strong leaders" who "are building a genuine and robust security alliance."
Polish Defence Minister Władysław Kosiniak-Kamysz hailed "a very important statement from President Donald Trump regarding the upcoming decision on the location of a permanent US military base in Poland."
In a post on X, he said that "effective cooperation between the presidents" was "yielding positive results."
"This is a significant confirmation of our strategic partnership," he wrote. "I am grateful for all efforts toward establishing a permanent American base in Poland. We are working together for our security."
Poland has pushed for a larger allied military presence on NATO's eastern flank since Russia invaded neighbouring Ukraine in 2022. The country currently hosts US troops on a rotational basis.
Kosiniak-Kamysz said on Tuesday that the rotational presence of US troops could become permanent "in a matter of weeks."
He told broadcaster Polsat News that a Pentagon review of the US military presence in Europe, being conducted under Defence Secretary Pete Hegseth, was expected to be completed around November or December, or by early January at the latest.
Kosiniak-Kamysz said Poland offered "the best conditions" for permanently stationing US troops and was prepared to cover the costs of infrastructure investment.
"Poland is ready to bear the financial costs of investing in its security through a permanent US military presence," he said. "Nobody else in Europe offers this to the same extent."
A US delegation visited Poland last week, including Thomas DiNanno, undersecretary of state for arms control and international security, and William Cappelletti, deputy assistant secretary of defence for European and NATO policy.
The talks covered a potential permanent US military presence in Poland, a proposed Patriot missile service centre and possible joint Polish-US investment projects in the defence industry, according to Polish officials.
Polish deputy defence ministers also briefed the delegation on Poland's defence industry and potential locations for a permanent US military presence.
Kosiniak-Kamysz put the cost of infrastructure at between PLN 15 billion and PLN 17 billion (EUR 3.9 billion, USD 4.5 billion).
Kosiniak-Kamysz said in June that the Pentagon was open to Poland's proposal for a permanent US military presence and that talks were progressing.
Kosiniak-Kamysz is set to meet with Hegseth in Washington next week for talks on Poland's security, including plans for a facility to service PAC-3 missiles used by Patriot air defence systems.
(gs)
Source: IAR/PAP, Reuters