According to talkSPORT, he told Sky Italia on Tuesday:
"There's nothing to it. I cannot either confirm or deny something that doesn't exist.
"I want this matter over and done with now. What's important for me right now is to get to the end of the season with Juventus and try and win some silverware."
Indeed, Allegri has repeatedly been quick to shut down suggestions he could be heading to Stamford Bridge at the end of the season, per football writer David Amoyal:
The Blues will be searching for a new manager at the end of the season to take over from interim boss Guus Hiddink. They will almost certainly be hoping to recruit a proven manager—particularly as they gear up to rival Pep Guardiola's Manchester City.
Allegri, who has two Serie A titles to his name, could well be adding a third this season with Juventus once again challenging for the scudetto.
Indeed, with the Bianconeri's win over Frosinone on Sunday, Allegri has guided them to an impressive milestone, per Amoyal:
As well as restoring Juventus to their status as realistic challengers in the Champions League—which saw them reach the final last year, their first since 2003—Allegri has received praise for his tactical knowledge.
With the Old Lady facing a showdown with title rivals Napoli on Saturday, Amoyal highlighted why there are several reasons to relish the clash—and as beIN Sports' Matteo Bonetti noted at the end of last season, the players have responded well to his approach:
Unfortunately for Chelsea, it seems they will have to look elsewhere for their latest boss.
They still have a number of possible options including Atletico Madrid's Diego Simeone or former Chile coach Jorge Sampaoli, but it's a blow to have a quality candidate so firmly rule himself out of the running.