The Gunners were previously linked with the 21-year-old over the summer, however, the transfer never materialised due to a disagreement over the fee.
The Ukraine international has begun the 2022-23 campaign in excellent form, contributing five goals and seven assists in 10 appearances across all competitions.
According to the Daily Mail, the Premier League leaders are still interested in signing Mudryk, and they are believed to be at the head of the queue to secure his signature.
The North Londoners could face fierce competition from AS Roma and FC Shakhtar Donetsk.
Mudryk has a contract until December 2026, and has recently admitted his dream to play for a Premier League club.