But the Dutchman could first take a job at this summer's World Cup finals, with Nigeria, Ivory Coast and North Korea all hoping to tempt the 63-year-old.
Hiddink had previously said he would not coach another team at South Africa out of respect for the Russia side he led to a play-off defeat by Slovenia in November.
Final lap: Hiddink is under contract with Russia till mid-July
But he could be set for a U-turn following his decision not to renew his contract as Russia boss.
Former Russia star Valery Karpin, now the coach of Spartak Moscow, hasled calls for Hiddink to be replaced as soon as possible rather thanallow his £500,000 a month contract run down till mid-July.
Successor? Giovanni Trapattoni (left) has been tipped to take over from Hiddink as Russia boss
'It is right to announce the decision now, but where is the sense in waiting to start the reign of the new national team coach? He needs to start work as soon as possible,' said Karpin.
Hiddink can expect plenty of suitors for a position after the World Cup. The former Chelsea manager has expressed a desire to return to England and would be the front-runner for the Liverpool job if Rafa Benitez takes over at Juventus.
But Turkey are pushing him to become their next manager, though their reported four-year contract worth £3.25million a year is about half his current salary.
Republic of Ireland boss Giovanni Trapattoni is said to be on a short list of candidates to replace Hiddink at Russia, but Dynamo Kiev manager Valery Gazzaev is seen as the frontrunner.
Tottenham Hotspur striker Roman Pavlyuchenko credits the third-place finish at Euro 2008 under Hiddink as the reason he got the opportunity to play abroad.
Highlight: Andrey Arshavin celebrates scoring against Sweden at Euro 2008, alongside Roman Pavlyuchenko (left) and Konstantin Zyrianov (right)
'Guus leaving is a great loss for the Russian football,' the striker told Russian newspaper Sport Express. 'By and large it is he who made Europe watch our national team and our players, giving us the chance to play in the leading European championships.
'We had a wonderful team and its main feature was wonderful atmosphere. And now the national team will be different, I hope I will not be worse only better.
'He is an excellent coach and a good person and such a combination is rare. Probably I will think of the time I worked with the Dutch as the best moments of my career.'
Arsenal star Andrey Arshavin believes his compatriots will regret the loss of their boss.
'I am thankful to Guus for our mutual work,' said the Russia captain. 'I think that all my team-mates pity now that he will depart.
'Hiddink spent a lot of time with us and did his best for more than three years. We owe him our greatest achievement in our careers: bronze medals of the Euro 2008.'
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