"FC Shakhtar president Rinat Akhmetov and Chelsea co-owner Behdad Eghbali discussed Mykhailo Mudryk's transfer to Chelsea FC today," tweeted Shakhtar.
"Parties are very close to agreeing on player's transfer to the club."
Mudryk, 22, has scored seven goals in the Ukraine championship this season.
British media claim the deal for the Ukraine international would be worth around €100 million over a seven-year contract.
Chelsea are currently struggling in 10th place in the Premier League.
Thursday's 2-1 defeat to Fulham was their seventh loss in their last 10 games in all competitions.
Chelsea said in a statement they were "discussing terms" with Shakhtar.
"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," the statement added.
Mudryk, who has played just 65 club games across his career to date and had earlier linked with a move to Arsenal, was named Shakhtar's player of the year on Saturday.