The 25-year-old Uruguay international has emerged as the north London club's top priority, following a glowing report from chief scout Steve Rowley.
After watching his side fall 11 points off the pace in the Premier League title race, Gunners boss Arsene Wenger will attempt to save his season, as pressure builds on the frugal Frenchman to splash the cash in a bid to end the club's eight-year wait for a major trophy.
Rowley watched Cavani score all four of Napoli's goals in Thursday's 4-2 Europa league victory over Ukrainian side Dnipro Dnipropetrovsk, prompting him to shoot up the shortlist of prospective New Year targets.
However, Arsenal will face a serious fight to convince him to come to the Emirates Stadium, after the South American striker signed a new five-year deal at the Stadio San Paolo in May.
With 78 goals in 109 matches for Napoli, Cavani is currently chasing down a 115-goal record set by club legend Diego Maradona, and has vowed to stay with the Serie A side until he surpasses that feat.
Thursday's goals helped him to his sixth hat-trick for the Azzuri, while Arsenal stumbled to another disappointing result, following a 3-3 home draw against Fulham on Saturday.