Hiddink said after Wednesday's 1-0 defeat by Slovenia, which knocked Russia out of next year's finals in South Africa, that he would decide his future in the next few months.
The Maribor fiasco was a bitter end for the 63-year-old Dutchman, who failed to guide his team to a major tournament for the first time in his career.
Hiddink led his native Netherlands (1998), South Korea (2002) and Australia (2006) to the World Cup and also steered Russia to the Euro 2008 semi-finals.
On the flight back to Moscow, the players pleaded with the coach to stay on and continue his Russian journey.
"It was very emotional when the team came to me to talk," Hiddink told reporters. "I was touched by it very much."
The team itself is likely to undergo major changes next year with several veterans considering international retirement.
UNCERTAIN FUTURE
"Several players are thinking of ending their careers in the national team," CSKA Moscow defender Sergei Ignashevich, 30, wrote on his personal website.
"The future of the entire Russian football looks very uncertain at the moment."
The immediate impact of missing out again on football's greatest spectacle will be felt in the coffers of the Russian FA (RFU).
The money would have come in handy, especially after the RFU's sponsorship revenues dried up significantly in the past year because of the global financial crisis.
The federation, itself, is facing big changes next year, with Sports Minister Vitaly Mutko announcing this week that he was stepping down from his dual role as RFU president.
Mutko, a former St Petersburg politician and a close friend of Prime Minister Vladimir Putin, was forced to resign after President Dmitry Medvedev demanded last month that all government officials in charge of various national sports bodies should be replaced by professional personnel.
Hiddink said last week that he would support Sergei Kapkov, an associate of Chelsea's billionaire owner Roman Abramovich, who has emerged as the front runner to replace Mutko.
But after the Slovenia defeat, some RFU insiders said the Kremlin might look elsewhere and pick former Zenit St Petersburg president Sergei Fursenko, another friend of Putin, for the job.
The World Cup flop might also have a negative effect on Russia's bid to host the game's biggest tournament in 2018.
"The consequences of our failure in Slovenia will be felt in many different ways," a source within the RFU, who spoke on condition that he was not identified, told Reuters.
"But I see at least one positive thing emerging from it after all as Hiddink might decide to continue as Russia coach because Guus is a winner and he wouldn't want to end his stay here on a losing note," the source said.
