The Dutch coach has won six of his seven games since taking charge of Chelsea last month.
Hiddink agreed to replaced sacked Luiz Felipe Scolari until the summer after the Russian Football Union allowed him to combine both roles.
Several members of the Chelsea squad have since urged the Dutchman to extend his stay but so far the 62-year-old has remained steadfast in his desire to resume his full-time duties with Russia at the end of the English season.
However, Hiddink admits there is a clause in his agreement with Russia that he could leave if he fails to lead the nation to the 2010 finals in South Africa.
"I will focus on Russia after this project but people say, 'Think about it, stay'," said Hiddink. "I enjoy it with the Russians but I do have a clause that says we can stop in November if Russia don't qualify. Then, the Russian FA can choose another direction and I would also be free to go."
Hiddink's Russia are second in World Cup qualifying Group Four, four points behind leaders Germany with a game in hand.
Meanwhile, Hiddink has been given a boost ahead of Saturday's Premier League clash with Tottenham at White Hart Lane.
Ivorian striker Didier Drogba returned to training after collecting a knock on his knee in the 1-0 win over Manchester City last Sunday.
"When you are injured for long periods it is difficult sometimes to come back to your level in a few weeks. It takes time but I just needed to play and that wasn't the case – but that is football," said Drogba.
"I think I am in good form at the moment. Back to my best? I don't think so but maybe not far. I really feel good and I really enjoy being on the pitch and playing.
"When you are out for a while and this is what you do best, it is difficult to be out. Now every moment I spend on the pitch, I try to enjoy and to give everything because I know maybe tomorrow I can get an injury and be out again for a while."
Drogba's return from injury earlier in the season was further complicated by suspension and a personality clash with former manager Scolari.
It culminated in a dreadful performance against Manchester United in January that prompted Scolari to axe the Ivory Coast international from the squad.
But Drogba is keen to point out that his poor form was down to a lack of match fitness and not a sign that he was fed-up with life at Stamford Bridge.
"Nobody can complain about my commitment," added Drogba. "Players are different, it is like the five fingers on the hand – all different but they shine in different ways.
"I don't have any problem for another player to be more popular than me. I am not looking for this. I just try to have a great life, enjoy what I am doing and make people around me happy."
Drogba has rediscovered his goal touch under Hiddink but his own upturn in fortunes has been matched by the rejuvenated spirit within the dressing room.
"Team spirit has always been good but when you lose it is difficult for people to get a smile on their face," said Drogba.
"When you win it makes things easier and everybody is more relaxed and comfortable."