The works owned by Aven have been lent to the Jewish Museum in Moscow, the Tate in London, the Museum of Modern Art in New York and recently the Royal Academy for its Russian art exhibition this year.
In the future, Aven dreams of a private museum to house his works, Financial Times reported.
He believes they would be overshadowed by other state collections if it were in Moscow, and in London he questions whether there would be sufficient interest. Instead, he is considering Riga, for which he retains an affinity because of his Latvian grandfather.
While his collection is mainly comprised of Russian art, it's slowly becoming international, he said.
"This was an all-Russian collection. Step by step it’s becoming international. I’m tempted by the connections between 20th-century Italian, German and Russian art, melded by the forces of totalitarianism," he told Financial Times.
Aven, the head of Russia's Alfa-Bank, most recently came into the public eye in early 2017 after BuzzFeed published an unverified dossier alleging financial ties and collusion between Vladimir Putin, Donald Trump, and several bank owners including Aven.
In 2015, Forbes named Aven among the five hundred richest people in the world, with a worth of around $5.1 billion.