The Daily Star says Chelsea have already had two bids for the 25-year-old rejected but are determined to get their man.
And the Blues are set to increase their warchest by selling Zhirkov to Russian side Anzhi Makhachkala for £12.5m. The 27-year-old has started just 16 Premier League games since moving to Stamford Bridge for £18m from CSKA Moscow in 2009.
And the cash raised from the Russian's sale is likely to go straight into an improved package for Modric, with Tottenham now weakening their hardline stance.
The Russian's departure also opens a foreign slot in Chelsea's squad for Modric.