"Parts of Georgia, Ukraine, Belarus, the Baltic States and Finland are states where Putin claims to have ownership.
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He added: "The West's leaders seem, from what they say, entirely to have forgotten that there are some leaders in the world who want to conquer other countries."
Mr Illarionov has helped draft a host of Russia's economic policies in recent years, and served as Mr Putin's personal representative at a number of G8 conferences. He is now a senior fellow at the Cato institute's Center for Global Liberty and Prosperity in Washington.
Finland is not a Nato member, meaning a Russian invasion would not be considered an attack against the alliance. The commander of the Finnish air force has said it has increased surveillance operations over the Baltic Sea in recent weeks.
The Scandinavian nation was part of the Russian empire for 108 years as an autonomous Grand Duchy. Asked if Mr Putin posed an immediate threat to what is now a stalwart of the EU, Mr Illarionov said: "It is not on Putin's agenda today or tomorrow.
"But if Putin is not stopped, the issue will be brought sooner or later. Putin has said several times that the Bolsheviks and Communists made big mistakes. He could well say that the Bolsheviks in 1917 committed treason against Russian national interests by granting Finland's independence."
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On the subject of what can be done to stop the progress of Russian expansion, Mr Illarionov said sanctions had helped rather than hindered Mr Putin because they "confirm his view of the world" - and that of "the Kremlin's propaganda".
"We must offer resistance by all means available," he said. "I'm not a bloodthirsty person, but there is sometimes no other way than military power to stop an opponent. The only answer to pure aggression is demonstrating willingness to offer a collective defence."
- UK Independent