According to British media, the deal will be worth 85 million pounds, with the Mudryk set to sign a seven-and-a-half-year contract.
Shakhtar said the clubs were very close to tying up a deal.
"Should a deal be agreed between the two clubs then the Ukrainian international, who can operate as a winger or a forward, will discuss personal terms with the Blues ahead of a permanent transfer," Chelsea said in a statement.
Mudryk was on his way to London for a medical on Saturday, Sky Sports reported.
It had been widely reported earlier in the week that Mudryk was close to signing a deal with Chelsea's Premier League rivals Arsenal - with a deal allegedly all but agreed.
It seems that Chelsea have beaten the Gunners to the young talent's signature at the 11th hour.