Mr Putin was asked during a discussion about the Arctic in northern Russia if he would be keen to hold his first meeting with Mr Trump if Finland hosts an Arctic summit after it becomes chair of the Arctic Council in May.
"Both side should prepare such events. If that happens, then we would be glad, I would be glad, to take part in this event," Mr Putin said in televised comments.
"Finland has great experience in organising important events of this type... Finland is a very fitting country, and Helsinki is a fitting location for such events."
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.
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