"Of course we will accept the registration when it appears, just as if we would with the Greeks, Germans, Spaniards or Dutch," said Warsaw Mayor Hanna-Gronkiewicz Waltz, adding that the city has not yet received such a request.
A spokesman for a Russian fan organisation told a Polish television station it would apply to register a march through the Polish capital to the National Stadium where Russia face their Group A rivals.
June 12 is a national holiday in Russia.
The relationship between the two countries, already strained by their common history, energy and security disputes, has been further soured by charges from Poland's rightist politicians that Russia was at least indirectly responsible for a plane crash that killed Polish president Lech Kaczynski two years ago.
Russia blamed the pilots for the accident in which all 96 passengers and crew perished on April 10, 2010, in western Russia. Poland said some of the responsibility rested with the ground controllers at the tiny Smolensk airport.
Last month, Russian officials rejected calls to move their squad from a hotel adjace nt to the presidential palace - a rallying site for groups accusing Moscow of a cover-up related to the plane disaster.
