The Hungary international only joined Dinamo from Anzhi Makhachkala in January 2012 but reports in his homeland suggest he is ready to move on to the Premier League.
The 26-year-old's agent Jozsef Vorosbaranyi denies those claims and has stressed that his client will be staying in the Russian capital.
"We read this rumour and could not comprehend it," Vorosbaranyi told Nemzeti Sport.
"Balazs Dzsudzsak is a Dinamo player and we deny these rumours that he'd leave Moscow. These false stories can be harmful."
But the words of Vorosbaranyi contrast with those of the player, who claimed just two weeks ago that he was ready to leave.
"I wouldn't mind changing," Dzsudzsak had told Nemzeti Sport.
"But only if it suits my club, my aims and my progression. I've been living for a long time in Moscow and honestly it's difficult for me to adapt.
"Seventeen million people live here and they keep rushing to get somewhere. My days are just about training and sitting in my car in a traffic jam.
"My dream is to play for a German or Spanish team. People are talking about some rumours but I've never cared about the gossips."