Premier League leaders Arsenal had a €65 million (£56m) bid for Mudryk rejected last week and sources have said that the Gunners have returned with a second offer in an effort to force a deal through.
But with Arsenal unwilling to meet Shakhtar's €100m (£88m) valuation of the 21-year-old, Chelsea have now opened talks with the club in an effort to negotiate a deal for the player.
Sources have said that Chelsea will hold further talks with Darijo Srna, Shakhtar's director of football, in London later this week.
Chelsea have spent £274m on new players since being taken over by a US consortium led by Los Angeles Dodgers co-owner Todd Boehly last summer and are close to breaking the £300m barrier with an agreement in place to complete a £33.6m deal for AS Monaco's Benoit Badiashile.
But while sources have said that Arsenal are still determined to complete a deal for Mudryk, Chelsea's attempt to hijack their bid has raised the prospect of the player's valuation being inflated further and potentially pricing Arsenal out of the market.