According to media reports in England, the 49-year-old has been earmarked as a potential successor to Gunners boss Arsene Wenger, whose contract expires at the end of the season.
Allegri will take charge of his 100th Serie A match with the champions on Sunday when they visit Cagliari, but while the personal milestone means little to the former AC Milan boss, he suggested that he would be happy to stay in Turin for many years to come.
"I can't deny anything I've never said or confirm something that does not exist," he told a news conference when asked about the Arsenal rumours.
"I'm fine here, I still have a year and a half on my contract. In due time, we'll sit down and discuss things with the board, which is the normal thing to do.
"I never thought about it [100 matches] because I am not interested in records but rather in winning the Scudetto and going all the way in the Champions League.
"I hope there are another 300 or 400 games, as I am happy at Juventus. I always said that, if I were to leave, Juve would be the first to know."
"We face a Cagliari side who score a lot of goals at home, who are quick and have managed good results against great teams," he said.
"It's a delicate moment of the season. We need to keep a distance between us and Roma and Napoli. This year, we've not managed five victories in a row in the league and that will be our aim."
The match comes at the end of a week in which tempers have flared between Juve and Inter in the wake of the league leaders' 1-0 win last Sunday.
Juve director general Giuseppe Marotta criticised Inter for focusing on what they considered to be debatable refereeing decisions during the match, prompting the San Siro side to release a stinging statement in response.
Allegri, however, was not interested in continuing the feud.
"Juve deservedly won a match against Inter," he said. "I still maintain that Inter are a good side who, fortunately for us, had a bad start to the season, otherwise they'd be challenging for the Scudetto. I won't add anything to that topic."