A spokesman at the commission could not immediately confirm the report. President Vladimir Putin is constitutionally barred from seeking a third term.
Meanwhile, opposition activists vowed to hold a weekend protest march that Moscow authorities have banned.
Opposition groups, including the radical National Bolshevik Party and the liberal Union of Right Forces, have joined Kasparov's United Civil Front to organize the march on Saturday to protest recent electoral law changes and what they say is the Kremlin's growing authoritarianism.
City officials have proposed allowing a meeting but not a march, which organizers hope to hold along one of Moscow's main streets.
Sergei Uldatsov, of the Red Youth Avant-garde, said that if authorities "resort to violence to prevent this it will be proof that authorities have lost their legitimacy."