The Gunners have their eyes on Mee, according to Alan Nixon of The Sun, who also added Arsenal's north London rivals Tottenham Hotspur are in the mix. Nixon said Burnley would ask for "around £20 million" for the defender, who has one year remaining on his deal.
Arsenal's interest in Mee makes sense given the sharp contrast between the defensive records of the two clubs. Mee has been the cornerstone of a Burnley back line breached just 26 times in 30 Premier League games this term.
It's the division's fourth-best mark, while the Gunners have shipped an eye-watering 41 goals during the same number of matches. Fortifying a back line lacking pace, aggression and talent has to be Arsenal's priority this summer.
Mee fits the bill thanks to the strides he's taken on the watch of Clarets manager Sean Dyche. Together with the equally impressive James Tarkowski, Mee has formed a partnership that is dominant in the air and formidable on the deck.
The 28-year-old is also sufficiently experienced to handle the step up to a bigger club, one hoping to be competing in next season's UEFA Champions League. Doing so would require Arsenal to win the UEFA Europa League, a daunting task given their issues at the back.
The main issue is in central defence, where both Laurent Koscielny and Shkodran Mustafi lack pace on the turn. Neither is physically imposing, particularly in the air.
Koscielny is 32 and continues to be blighted by Achilles problems, while the 33-year-old Per Mertesacker is set for retirement.
Arsenal need a refresh in central areas, a process signing Mee would accelerate. He could become the steady presence the Gunners have missed at the heart of the defence since the days of Sol Campbell and Kolo Toure.
Beating Spurs to Mee's signature may not be easy, though. Unlike the Gunners, Tottenham look likely to be playing Champions League football next season—they sit fourth in the league, 13 points ahead of Arsenal and five in front of fifth-place Chelsea.
Mee isn't the only centre-back north London's warring neighbours could compete for this summer. The Daily Telegraph's Matt Law recently reported both clubs will consider signing Jonny Evans for just £3 million, provided West Bromwich Albion are relegated.
Pairing either Mee or Evans with a younger, quicker option would turn the weak point of the Arsenal squad into one of its strongest.