"We're fully satisfied with the work of the coaching staff headed by Hiddink," Anzhi general director Aivaz Kaziakhmedov told the club's website.
Kaziakhmedov said he had been forced to make a statement following reports in Russian and foreign media that Anzhi bosses were unhappy with the 66-year-old Dutchman.
"We're very disappointed with numerous hasty and often false comments in the media, made by so-called 'experts' who had never in their lives even come close to those trophies that have been won by Hiddink and many of our players," said Kaziakhmedov.
"Anzhi are a young team, only in the process of becoming a top-notch side capable of achieving great results."
Hiddink's team, boasting several world-class players such as Cameroon striker Samuel Eto'o in their expensively-assembled squad, are having their best season in Russia's top flight.
The club from the volatile North Caucasus region, bankrolled by billionaire owner Suleiman Kerimov, are third in the league, having also reached the Russian Cup semi-finals.
Media reports said Hiddink, who surprised many pundits by guiding outsiders Russia to the Euro 2008 semi-finals, could be sacked after Anzhi had one win in eight matches.
Anzhi, who trail leaders CSKA by 10 points and champions Zenit by seven with four games left, host Rubin Kazan on Saturday.
- Sports & Recreation