The Gunners have identified the 22-year-old as their top target for the January transfer window.
The North Londoners allegedly had bids of £55m and £62m rejected, as the Ukrainian outfit hold out for a fee closer to their £88.8m asking price.
According to the Evening Standard, the Premier League leaders are closing in on an agreement to sign Mudryk in a deal that would result in the club paying around £60m up front.
If the deal goes through, Mudryk would bolster Mikel Arteta’s attacking options, with Gabriel Jesus and Reiss Nelson currently out of action with injuries.
Mudryk has been in sensational form for Shakhtar this term, contributing 10 goals and eight assists in 18 competitive appearances.
The Ukraine international has a contract with Shakhtar until 2026.