The Dutchman, whose existing contract expires in summer 2010 following the finals, had announced towards the end of Russia's qualifying campaign that any questions about his future would be dealt at with at a later stage.
However, with Russia's World Cup campaign now at a premature end thanks to yesterday's 1-0 defeat in Maribor, those questions have been hastily brought forward, although the Dutchman, for now, is remaining tight-lipped.
He said: "I have an existing contract until the end of the World Cup finals in July 2010. The question [of whether I will continue to UEFA EURO 2012] will require some time for thought. Before the matches with Germany and Slovenia the Russian Football Association (RFS) expressed their desire to continue working together. But we'll talk about the future at a later stage."
Hiddink took over as coach in 2006 and guided Russia through a difficult qualifying group involving England and Croatia to an historic semi-final place at the 2008 UEFA European Championship.
However, having enjoyed varying degrees of success at FIFA World Cup with the Netherlands, Australia and South Korea, failure to qualify on this occasion with Russia will prove an unwelcome blot an otherwise illustrious record for the Dutchman, who turned 63 earlier this month.