Spurs boss Conte slams 'disrespectful' links to Juventus
"It is incredible in this period. I think this is disrespectful for the coach that works in Juventus, and it was disrespectful for me working for Tottenham," Conte said, according to James Olley of ESPN.
Allegri's future has become uncertain after Juventus managed to win only two of their opening Serie A matches this season.
Meanwhile, Conte, who coached Juventus from 2011-14 and won three Serie A titles, was reluctant to offer an update on possible contract negotiations with Spurs. His deal is set to expire after the campaign.
"We have just started the season," he said. "Many times I spoke about this topic, and I always said I'm happy and enjoying my time with Tottenham. Then, we have the whole season to find the best solution for the club, for me.
"For sure, I am enjoying the time to work in Tottenham. I have a great relationship with the owner, with (football managing director Fabio) Paratici. I don't see problems for the future.
"Now it is important to be focused. We signed the contract because both parts agreed to sign the contract, and for this reason, I don't see a problem in this moment. I don't want in the future to listen to someone speaking about this because I repeat: this is disrespectful for another coach and also for me."
Tottenham sit third in the Premier League with 17 points from seven games ahead of the north London derby against Arsenal on Saturday.