Trump's remarks came hours after Kremlin said the two leaders will get together "in a third country," with the date and venue to be announced Thursday.
The idea of a Trump-Putin summit, floated for months, comes amid still strained ties between Washington and Moscow, with little solid outcome expected by experts.
Following the announcement by the Kremlin, Trump told reporters at the White House that he will "probably" meet Putin after attending the NATO Summit in Brussels on July 11-12.
The location could be in Helsinki or Vienna, he added.
Trump last met Putin in Vietnam on the sidelines of an Asia-Pacific summit in November.
The announcements from both sides came after Putin's meeting with visiting US National Security Advisor John Bolton in Moscow.
Bolton's visit reflected "the continued desire of the Trump administration to improve relations with Russia," Dan Mahaffee, senior vice president and director of policy at the Center for the Study of the Presidency and Congress, told Xinhua.
Mahaffee said Trump, emboldened by his "negotiating successes," felt that he can move forward on meetings with Russia.
Trump has been seen as caring about maintaining good personal relations with Putin while bilateral ties kept sinking due to Russia's alleged meddling in the 2016 US presidential election and the two countries' diplomatic spats, among other thorny issues.
"Trump has great faith in personal diplomacy," Brookings Institution Senior Fellow Michael O'Hanlon said.
"Trump likes Putin and feels the United States should have close relations with Russia," another Brookings Institution Senior Fellow, Darrell West, told Xinhua. "He doesn't worry much about foreign meddling.
The investigation of alleged collusion between Team Trump and Russia during the election in 2016 passed its one-year anniversary last month, with the White House continuing to dismiss the claim.
So far, several individuals have been indicted as a result of the investigation. However, none of the charges relating to US citizens or Team Trump has directly accused anyone of working with Moscow to meddle in the presidential campaign.
WHAT TO EXPECT
Trump told reporters on Wednesday that he will talk about Syria and Ukraine with Putin, as well as other issues.
But experts expect the meeting to yield little result, as the Washington-Moscow antagonism is complicated.
O'Hanlon does not see any specific plan or agenda for the upcoming summit.
West said not much room has been left for negotiation, "given Congressional hostility to any deal."
"Both Republicans and Democrats will oppose easing sanctions and Putin will not make any deal without that," he said.
Last August, Trump signed a bill to impose sanctions on Russia that won a sweeping majority vote in both houses of Congress. Afterward, the Trump administration also unleashed a string of sanctions over Russia's allegedly "threatening" activities against the United States.
Earlier this month, Putin signed into law a bill which allows him to respond to sanctions by the United States and other "unfriendly states."
However, Putin said on Wednesday that Russia never seeks confrontation, and he believed the icy relation was largely the result of the acute domestic political struggle in the United States.