Per BBC Sport's David Ornstein, Allegri is on the Gunners' shortlist of candidates to replace the outgoing Arsene Wenger and was spoken to by Arsenal, though it is unknown if they contacted him "directly or indirectly."
However, Allegri has given assurances that he will likely stay put in Turin. According to James Benge of the Evening Standard, he said: "There is a very high percentage, I've never had any doubts. Next week I will meet the board to plan the future."
His comments echo those he recently made about his future and the likelihood of him staying on at Juventus, per BBC Sport:
Allegri is contracted to Juventus until 2020, and given all he has accomplished with the Bianconeri, they most likely want him to stay.
BT Sport Football offered a look at his success with Juve:
Football on BT Sport @btsportfootball
2015: League & cup double 🏆🏆 2016: League & cup double 🏆🏆 2017: League & cup double 🏆🏆 2018: League & cup double 🏆🏆 Max Allegri has confirmed he's staying at Juventus next season. "Next year will be even more difficult and we need to keep raising our game." ⚫️⚪️ https://t.co/9IgN9p1V0Z
On top of that, he also guided the Old Lady to the 2015 and 2017 UEFA Champions League finals, albeit Barcelona and then Real Madrid would stand in his way of victory.
His track record is equally what would make him so appealing to Arsenal, who will hope Wenger's replacement can take the club back to the pinnacle of English football and become a contender on the European stage once again.
The Gunners exited the Champions League in the round of 16 for seven consecutive seasons, while this year they were knocked out of the UEFA Europa League in the semi-final by eventual winners Atletico Madrid.
With Allegri set to stay put for the time being, Arsenal will need to look elsewhere for their next boss.