Allegri, 49, has been linked with the Arsenal post, which will become vacant at the end of the season if current boss Arsene Wenger doesn't sign a new contract.
Arsenal are said to have earmarked a number of candidates to replace Wenger should the Frenchman step down, with Allegri on that list.
It emerged the Italian boss is taking English lessons, which has fuelled speculation that he could be heading to the Premier League this summer.
But while Allegri did confirm he is learning the language, he insisted he has no intention of leaving Turin.
"It's true, I'm studying English, but certainly not to go to Arsenal," he told Italian newspaper Gazzetta dello Sport.
"Here at Juventus I'm fine.
"The funny thing is that I have been to London but on holiday with my daughter - and on the same day I arrived in England there was a photo of me on the Sun.
"If Juventus are going to change their coach, just let me know."
Arsenal boss Wenger appears in no hurry to sign a new contract at the club, despite the Gunners board being happy for him to continue after two decades in charge.
And Wenger's decision on his future could have a major impact on the squad, with star man Mesut Ozil already confirming he will wait to see what the manager does before committing to a long-term new contract.
Likewise, Arsenal have a handful of players out of contract in the summer of 2018 and will have to tie up those extensions by the end of the season at the latest.
As for Allegri, he joined Juve in 2014 when now-Chelsea manager Antonio Conte quit the Turin club to coach the Italy national side.
Allegri has won the Serie A in both of his seasons in charge of Juve, while he took the team to the Champions League final in 2015.
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