Allegri, who has won the Serie A and Coppa Italia double in each of his two seasons at Juve, had been strongly rumoured to be a frontrunner to succeed Arsene Wenger should the Frenchman depart the Emirates Stadium at the end of his contract, which expires following the 2016-17 campaign.
But after seeing Juve remain on track for the treble by beating Napoli 5-4 on aggregate in Wednesday's Coppa Italia semi-final at Stadio San Paolo, Allegri committed his future to the club.
"My intention is to continue with Juventus, because I am happy here," Allegri said after his side's 3-2 loss on the night.
"I haven't met with the club yet, as there are other priorities, but then we'll sit down and evaluate things.
"This team has great potential, a mixture of experience and youth. Above all Juventus are a top-level club and there are few out there who could be considered better."
Juve struggled to hold Napoli at bay despite Gonzalo Higuain scoring twice against his old club, but Allegri insisted he was not concerned by his team's performance.
"It's a good result, especially after two very tough games," Allegri said. "We played better compared to Sunday [a 1-1 league draw at Napoli], then made life complicated for ourselves with the error [by goalkeeper Neto] for 2-2.
"We didn't have the strength to pile forward anymore and I had no real substitutes left, but overall it was a good performance and we ran few risks after going 3-2 down. It was a game we could've won, but the objective was to reach the final.
"Higuain had a good week of work on international duty and you can see how hard he trained, because he looked really sharp in front of goal. Overall it was a good performance and I am not worried, because we were the ones who let Napoli back into the game."