Allegri guided Juventus to his fourth consecutive double of Serie A title and Coppa Italia, and their seventh straight Scudetto in total. But there had been question marks over his future in Turin with Arsenal poised to pounce.
The 50-year-old has sought to lay these rumours to rest as he said that his chance of staying at Juventus was the "highest", before outlining his plans to start work ahead of next season.
"Next week, I'll meet with the club as we start to make the team competitive again just like every year," said Allegri, as quoted by Sky Sports News.
"Next year will be even more difficult and we need to keep raising our game. It's in Juve's DNA to be competitive on all fronts.
"It's always our objective to work hard to create Juventus history. That boils down to determination, sacrifice and confidence in our own abilities.
"It's in the difficult moments that I actually have more fun."
Allegri is another candidate to fall by the wayside and it now seems increasingly likely that Manchester City assistant manager Mikel Arteta will be replacing Wenger at the Emirates Stadium.
Arteta is a former Gunners captain who played for the club between 2011 and 2016. He has been strongly linked with the Arsenal vacancy and City are reportedly resigned to losing the Spaniard now.
Allegri's Juventus finish their season against Verona on Saturday in what will the final game of Gianluigi Buffon's 17-year Bianconeri career.