Mr Trump is trying to create a united front against Kim Jong-un and wants Mr Putin to join the leaders of Japan and South Korea in pressing China to do more to reign in the trigger-happy despot.
The US President said: “I think it’s expected that we will meet. We want Putin’s help on North Korea.”
Kremlin spokesman Dmitry Peskov had earlier acknowledged there was currently no co-operation between Russia and US on North Korea.
Mr Peskov said: “There is no cooperation so far. Only periodic exchanges of views.”
He said there was a “great probability” that the two leaders would discuss the situation on the Korean peninsula if they met.
vCard.red is a free platform for creating a mobile-friendly digital business cards. You can easily create a vCard and generate a QR code for it, allowing others to scan and save your contact details instantly.
The platform allows you to display contact information, social media links, services, and products all in one shareable link. Optional features include appointment scheduling, WhatsApp-based storefronts, media galleries, and custom design options.
The most likely venue for a meeting would be an Asian economic summit in Vietnam next week.
Mr Trump has ramped up his tough rhetoric against North Korea after arriving in Japan for a 12-day trip – the longest Asian tour by a US leader since George HW Bush in 1992.
He warned that Washington and its allies are prepared to defend freedom and that “no dictator” should underestimate US resolve.
Meetings with Japanese Prime Minister Shinzo Abe come against a backdrop of heightened tensions over Pyongyang’s nuclear and missile tests.
A top aide said the president intends to tell Asian leaders the world is “running out of time” in dealing with the nuclear crisis on the Korean peninsula.
Mr Trump has rattled some allies with his vow to “totally destroy” North Korea if it threatens the US and his dismissal of North Korean leader Kim Jong Un as a “rocket man” on a suicide mission.
Speaking to hundreds of cheering US and Japanese troops at Yokota Air Base, just west of Tokyo, Mr Trump said: “No dictator, no regime, no nation should ever underestimate American resolve.
“Every once in a while, in the past, they underestimated us. It was not pleasant for them, was it?” said Trump, who wore a bomber jacket as he addressed the troops.
North Korea’s recent actions, including several missiles that flew over Japan and Pyongyang’s sixth and largest nuclear test, have raised the stakes in the most critical international challenge of Mr Trump’s presidency.
Recent drills over South Korea by two US strategic bombers have further heightened tensions.
He said: “We will never yield, never waver and never falter in defence of our freedom.”
He said decision would be made soon on whether to add reclusive North Korea to a list of state sponsors of terrorism but warned his administration planned to take a different approach after years of what he termed “total weakness.”
He said: “We want to get it solved. It’s a big problem for our country and the world, and we want to get it solved.
“And I hope it all works out for everybody.”