The Russia international was the Blues marquee signing when he joined from CSKA Moscow for £18million in the summer.
But injuries have hampered his development at Stamford Bridge, where he has managed just six Premier League appearances.
Squeezed out: Yuri Zhirkov (right) has found his first-team opportunities at Stamford Bridge limited behind Ashely Cole and Florent Malouda
Old pals: Dynamo boss Valery Gazzaev was Zhirkov's mentor at CSKA Moscow, the Russian's former club
The 26-year-old warned before making the switch that he would not be happy to be a bit-part player for the Blues, though he has been patient and positive while battling unexplained swelling in both his knees since moving to England.
Zhirkov started Chelsea's last two games, but assistant boss Ray Wilkins recently admitted he was behind Ashley Cole - 'the best left-back in the world' - while Florent Malouda is preferred on the left wing.
A recent audition in central midfield is likely to be short-lived once Michael Essien and John Mikel Obi return, so Kiev are ready to chance their arm.
The Ukrainian League leaders can still do business as their championship does not resume until the end of the month.
Kiev's Russian boss Valery Gazzaev nurtured Zhirkov at CSKA and would be keen to sign him for the rest of the season.
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