The Russian outfit have been strongly linked with the 27-year-old this month, but until now have remained tight-lipped over a proposed move.
However, despite their hopes of landing the former CSKA Moscow player, Dyakov admits they may struggle to outbid their wealthy compatriots from Russia's top flight.
"Almost all clubs from the Russian Premier League are interested in the signing of Zhirkov," he said.
"By now, we haven't contacted neither Chelsea nor the player. It can be suspected how much Anzhi [Makhachkala] or Rubin [Kazan] offered for the player so we know what his price may be around.
"Of course, Yuri would be an ideal choice to the left side of the Dynamo midfield and we would be glad to hear if he said he would like to join us very much.
"But fighting hand to hand for a transfer and overbid someone's offer - Dynamo won't do this. Don't expect us to explode the transfer market."
Source: Team Talk
Source: Team Talk