The Dutchman, who took on the role of interim Chelsea manager after Jose Mourinho's sacking last year, has been linked with the job in the wake of Russia’s poor campaign in France.
The Russians drew with England before losing to Slovakia and Wales to finish bottom of the group.
“If I can make a contribution, I’ll will be happy to do so,” he told Dutch broadcaster NOS. “Russia sit in a particularly complicated situation, not only in the sporting arena but also in terms of their image,” said the 69-year-old, who coached Russia from 2006 to 2010.
“Sport can help them, although it is perhaps my idealistic thinking, to project a better image out to the world.”
Russia are looking for a new coach after Leonid Slutski said he would not continue after they were eliminated on Monday.
"I think after a tournament like this, you need someone else to take charge of the national side at major tournaments," he said.
(Reporting by Mark Gleeson; Editing by Peter Rutherford)
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