John Teft said Tillerson would likely meet Russian Foreign Minister Sergey Lavrov and Putin "in the near future," according to Russian news agency Tass.
It said Teft commented during a lecture in the northern Russian city of Arkhangelsk.
US media reports suggest that Tillerson is likely to visit Russia in April but a date has yet to be announced.
The Kremlin has repeatedly refused to comment on the visit and declined to say whether Putin would meet Tillerson.
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