Kremlin spokesman Dmitry Peskov said the leaders suggested the Austrian capital during a phone call as far back as March.
Mr Peskov noted during a meeting in Qingdao, China, where the Russian President is attending a regional summit that “there have been no concrete agreements or understandings, and no specific discussions are being conducted now”.
The Russian President said today he hopes Moscow’s relationship with Washington improves.
The 65-year-old said: “I hope an improvement in ties also takes place.
“At any rate, we are ready for it. I think the ball is in the Americans’ court.”
A date for the meeting is yet to be set after the conflict in Syria and the poisoning of former Russian spy Sergei Skripal and his daughter Yulia in Salisbury, Wiltshire, angered Mr Trump and caused fragile relations to deteriorate.
In response to the April 9 gas attack in Syria that killed more than 80 innocent civilians, President Trump took to Twitter in a display of rage to blame Russia.
He told his 52million followers: “Russia vows to shoot down any and all missiles fired at Syria.
“Get ready Russia, because they will be coming, nice and new and ‘smart!’”
He added: “You shouldn’t be partners with a gas killing animal who kills his people and enjoys it!”
But in a bizarre twist, Mr Trump’s election campiagn is being investigated by America’s Special Counsel over a possible interference and meddling made by Russian hackers.
Mr Trump recently tweeted he had a right to “pardon himself” over the probe but added that he had done “nothing wrong” as enquiries continue.
He said: “As has been stated by numerous legal scholars, I have the absolute right to PARDON myself, but why would I do that when I have done nothing wrong?
“In the meantime, the never ending Witch Hunt, led by 13 very angry and conflicted Democrats (& others) continues into the mid-terms!”
One of his followers hit back with: “Innocent people never talk about their right to pardon themselves.”
Another added: “It says a lot that this is on your mind. Guilty conscience?”