The 51-year-old's current deal is set to expire in 2020, six years on from his appointment as Old Lady boss back in 2014.
He looks set to continue his winning streak this season, as the reigning Italian champions have once again pulled away at the top of the table, nine points clear of second-placed Napoli.
Meanwhile, in the Premier League, Man United are on the look-out for their next permanent manager after sacking Jose Mourinho earlier in December, with Ole Gunnar Solskjaer taking charge on a caretaker basis until the end of the current campaign.
Allegri has emerged as one of the favourites for the position, but he refused to be drawn on the subject when speaking to the media at a press conference on Friday.
"I have a contract with Juventus and I am happy here," he said to reporters. "We are doing a great job together with the fans. There are many games to win before the end of the season, there is time before June.
"Italian football is fascinating, I am not tired of it. I want to stay to improve Italian football.
"Outside this world, there are many things to be done, we need to involve the kids to build a better future for this game”.
The Juve manager was speaking ahead of his side's final game of 2019 this weekend against Sampdoria, with the winter break set to take effect thereafter in Italy.
The Bianconeri are unbeaten domestically this term and they can also look forward to a last-16 Champions League tie against Atletico Madrid in February.
United have also made the knockout phase with a scheduled showdown against Paris Saint Germain on the horizon, as Solskjaer looks to revive the team's dwindling fortunes on the pitch.
The Norwegian could become a candidate for the permanent job if he impresses between now and May, while Tottenham's Mauricio Pochettino has also been heavily linked with the role.