The Hungarian has been subject to previous interest from Liverpool and Inter Milan, but reports in Russia suggest that the Hammers have joined a number of Italian clubs in the hunt for his signature.
Dzsudzsak left Hungary in 2008 to join PSV Eindhoven, and was sold to Anzhi Makhachkala in 2011. After just one year with the club, he was signed by Dynamo.
"Balazs is very comfortable in Moscow and would like to perform for Dynamo," Jozsef Vorosbaranyi, the player's agent, told Isvestia newspaper.
"However, Dzsudzsak also wants to try his hand at one of the top European leagues.
"I hope the leadership of Dynamo will consider proposals."