The day after Advocaat resigned as Belgium coach, the ANP agency reported him saying he could not refuse the offer from Russia, who failed to qualify for this year's World Cup finals after losing a playoff to Slovenia.
"Russian soccer is of a higher level than Belgian soccer. It matches the level I'm used to working with. In addition, with Russia you have a chance to reach a European championship tournament if we qualify," Advocaat was quoted as saying by ANP.
"I'm 62 years old and getting a chance to go to Russia - I'm grabbing it," he said, adding that his lawyer was in negotiations with the Russian soccer association.
Russia's interest in Advocaat was "a big honour", he was quoted as saying by Russian newspaper Sport-Express.
Advocaat took over as Belgium manager in October last year with the goal of qualifying for the Euro 2012 finals but has resigned after just over six months in charge.
Belgium's football association said it was would seek legal advice to determine what action to take.
Advocaat, who coached Russian club Zenit St Petersburg to a UEFA Cup triumph in 2008, has been linked with the post since Hiddink announced in February he would step down when his contract expired in mid-year.
New Russian FA chief and former Zenit president Sergei Fursenko has made no secret of his desire to bring Advocaat back to Russia after the Dutchman led the club to their first league title in nearly a quarter of a century.
Fursenko had said last week that a new Russia coach would be named on May 17.
