Putin said he would be keen for their first face-to-face talks to happen at the G20 summit in July or earlier.
Speaking at an international forum on the Arctic organised by Russia in the northern city of Arkhangelsk, Putin once again denied any Kremlin involvement in the US election last year, slamming the recent accusations as "absurd" and "irresponsible."
"We are just waiting for when the situation improves," Putin said in televised comments. "When it's over, I hope we decide on holding a meeting" with Trump.
Putin said he would be keen for their first face-to-face talks to happen at the G20 summit in July or earlier, for example at a summit Finland may host after becoming chair of the Arctic Council intergovernmental forum in May.
"Such events should be prepared by both sides. If it happens, then we would be glad, I would be glad, to take part in this event," Putin said at the forum, which Finnish President Sauli Niinisto is also attending.
"If not, then such a meeting could take place within the framework of the usual meetings, at the G20," Putin added.
The G20 summit of world powers is set to convene in the northern German city of Hamburg in early July and both US and Russian leaders are expected to attend.
"We see the US as a great country with which we want to have a good partnership. Everything else is lies, inventions and provocations" used by "some political forces in the US... to strengthen their position," said Putin.
He slammed the scrutiny of the Russian ambassador to the US, Sergey Kislyak, whose meetings with Trump's associates figure in several congressional investigations into possible election meddling by Moscow.
"I can see the US ambassador (to Russia John Tefft) is sitting here... He is communicating with everyone," Putin told the audience at the forum.
"Meanwhile the contacts of our envoy are being limited, his every meeting is met with hostility as some kind of spy stunt," Putin said, insisting that Kislyak is simply doing his job.
"What else is he there for?"
US intelligence has accused Moscow of waging a broad-ranging campaign to help Trump win the election. This has led to investigations in the Senate and House of Representatives as well as an FBI probe into the Trump campaign's ties with Russia.
Trump's son-in-law and top aide Jared Kushner is to face a congressional panel over his contacts with Russian state bank executives last year that Moscow has dismissed as "normal business" for the banks.
Putin on Thursday said the Russia allegations are used as a way to prevent Trump from implementing his policies and accused the forces behind them as irresponsible.
"We can see what is happening, the president is being prevented from carrying out his policies," Putin said of Trump.
"It's not in the interests of the majority of American people to take US-Russian relations to the point of absurdity," Putin said.
"What do we want? To completely end all relations? They are already almost at zero."
"What do we want? To completely break off diplomatic relations? To take the situation to the 1960s, to the Cuban missile crisis?" Putin questioned.
"And then what? People who are this irresponsible, where are they leading us all?" Putin asked, without accusing anyone in particular.