"It was mentioned that Vienna could be such a city" Peskov was quoted as saying by the RIA Novosti state news agency after being asked if Putin discussed whether the city could hold such a meeting when he met with Austrian Chancellor Sebastian Kurz on Tuesday.
Peskov's comments come a day after Trump called for Russia to be readmitted to the group of the world's leading nations, known as the G7, a step that would end Russia's international isolation over its 2014 annexation of Crimea from Ukraine.
Speaking from China where Putin was attending a regional security summit, Peskov said that in their last telephone conversation on March 20 the Russian and US leaders had also mentioned possibly meeting in Vienna.
"You know, the two presidents discussed the necessity of holding such a meeting in their last telephone call. Including that Vienna could be such a city" for the summit, said Peskov.
He added, however, that no concrete agreements have been reached and no concrete discussions were underway.
Under the conservative Kurz, Austria has strived to act as a mediator between Russia and the West.
While the EU-state imposed sanctions on Russia over Crimea along with the rest of the bloc, Austria did not expel Russian diplomats like other Western nations following the March poisoning of a Russian former double agent and his daughter in Britain, an attack London has accused Moscow of being behind.
Putin said in a Russian television interview that a meeting with Trump would be "useful."
"Dialogue may prove to be constructive," he said in the interview, the full version of which was released on Saturday.
He added that Russia was ready to "develop, deepen and normalise ties with the United States," noting that the next move was for Washington to make.
Putin indicated that he did not like "a lot" of the US authorities' decisions but praised Trump for his consistency.
"Trump fulfils his pre-election promises," he said.
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