The 25-year-old has long been linked with a move to the Roman Abramovich-owned Blues, with former coach Guus Hiddink reported to have instructed the Russian to splash out on him this summer.
Liverpool boss Rafael Benitez was also thought to be pondering a move for the highly-rated left-sided player - dubbed the 'Russian Ronaldinho' - who impressed in Russia's run to the semi-finals of Euro 2008.
While Arsenal forward Andrey Arshavin was keen to see his fellow countryman become a Gunner, whose fans are hopeful of several experienced heads arriving at the Emirates Stadium to compliment a squad awash with talented starlets.
Zhirkov has repeatedly insisted he knows nothing of any deal involving Chelsea, and even recently revealed that he would rather join European Cup winners Barcelona instead.
However, The Times claim the Blues are now eager to push through a deal for the full-back, having lost out to Liverpool in the race to recruit Portsmouth defender Glen Johnson.
"I read the papers, listen to the radio and I am genuinely surprised, given that no actual offer from Chelsea exists," Zhirkov said earlier this month.
"It is very possible that I would say yes. But before that I would have to weigh up the pros and cons."
NEWS: Zhirkov: I want to sign for Barcelona
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