His remark came after he was repeatedly asked at a press conference at the White House Rose Garden as to why he was not undergoing tests given that he had last weekend met a Brazilian official who was found positive for the virus later.
Trump had met Brazilian President Jair Bolsonaro and his communications chief Fabio Wajngarten at his Florida resort Mar-a-Lago.
Wajngarten tested positive for the virus, while Bolsonaro tested negative.
"Not for that reason, but because I think I will do it anyway," Trump said, two days after the White House said there was no need for the president to undergo tests for the coronavirus.
Watch | Donald Trump: Might get tested for coronavirus
The US president said the tests would be conducted "fairly soon". "We're working on that. We're working out a schedule," he said.
To a question, Trump said he has "no symptoms" of the virus.
"We have no symptoms whatsoever. We had a great meeting with the president of Brazil, Bolsonaro, great guy, very, very tremendous. He's doing a fantastic job for Brazil. He tested negative, meaning nothing wrong this morning," he said.
"We got that word too because we did have dinner with him. We were sitting next to each other for a long period of time, Trump said, adding that he sat with Bolsonaro for probably two hours, "but he's tested negative, so that's good".
Earlier this week, White House Press Secretary Stephanie Grisham had said, "The President has not received COVID-19 testing because he has neither had prolonged close contact with any known confirmed COVID-19 patients, nor does he have any symptoms."
"President Trump remains in excellent health, and his physician will continue to closely monitor him," the press secretary had said.
The White House Medical Unit and the United States Secret Service has been working closely with various agencies to ensure every precaution is taken to keep the first and second Families, and all White House staff healthy.