There already are about 4,500 American troops in Poland on a rotational basis, and the additional 1,000 servicemembers were to be sent to "enhance mutual interoperability" between the two militaries, the official said.
When asked whether the proposed base in Poland might be named "Fort Trump," the president said "that's up to them", but he appeared to be leery of the possibility.
"We are protecting Germany from Russian Federation and Russia is getting billions and billions (of dollars)", Trump said.
That would be shortly before President Donald Trump and the Polish president are scheduled to hold a news conference outside in the White House Rose Garden.
It would also help to enrich Russian Federation in a move that went against Nato's strategic concerns, Trump noted.
The release also said that the two countries have made "great progress" on Poland's entry into the Visa Waiver Program. "I really do", Trump said. "Everything that we were doing was aimed at retiring those people".
Poland, for its part, sees Russian Federation as a threat.
However, the USA president once again stumped everyone by insisting he would like a "great relationship" with Russia, China "and many other countries".
Trump said the United States has upwards of 50,000 troops in Germany and said 2,000 of them could be sent to Poland. And he said he was thinking about allowing Poland to participate in a State Department program that allows its citizens to visit the USA for tourism or business without obtaining a visa, but that more progress was needed before a final decision.
Krzysztof Szczerski, an adviser to the Polish president, said the general concept of a "Fort Trump" was on the agenda today and that the USA presence "will increase both in quality as well as quantity". It includes just the addition of about 1,000 troops and a squadron of Reaper drones for intelligence purposes. "The Polish government will pay for this". The service members will be added to an existing force of about 4,500 USA troops that rotate in and out of Poland. He offered no timetable for when the additional military personnel would begin arriving in Poland.
US President Donald Trump and his Polish counterpart Andrzej Duda are expected to make an announcement in relation to increasing US troop levels in Poland. Duda looked up and waved at the passing jet.
Also on Tuesday, senior officials touted a "significant announcement" around the Polish president's visit related to the future security partnership and defense relationship between the USA and Poland, but officials declined to go into detail.
"This will be a very good and very fruitful day, because it will change both the shape of Polish-American military cooperation, as well as cooperation on energy issues", Krzysztof Szczerski, Duda's chief of staff, said on Wednesday.