The Hungarian was identified as a transfer target for both Merseyside clubs last summer, but no move materialised. He is reportedly unhappy in Russi, where he plays with Dinamo Moscow, and a move to the Premier League could be tempting.
Liverpool had a bid of around £12m turned down for winger last season and it is thought that a similar bid could see him move to Everton. As agents are want to do, Dzsudzsak's has already been touting his client to potential clubs.
He told Italian website cittaceleste.it; "Balazs Dzsudzsak has indicated his wish; he wants to change country but he's contracted to Dinamo Moscow."
Would you like to see Everton sign Balazs Dsudzsak? Vote and comment below.