Allegri's odds have come in with the bookmakers over recent days, placing him as favourite ahead of ex-Barcelona boss Luis Enrique, with Goal revealing that he is a leading contender for the role alongside Mikel Arteta.
Speaking ahead of the game, Allegri – who is contracted in Turin until 2020 – reiterated his satisfaction with his role and the Juventus board.
"I have a great relationship with the club and we are in sync, as has been demonstrated over the last four years," he told reporters.
"The team was turned inside out during the first season and the club worked so well to bring in players of quality, who had not just amazing technical skill sets but great human values.
"At the end of the day, in football you need more than technique to win. You need other values that can push you on during difficult times.
"I have a very good relationship with the management. As we do every year, we will sit down and discuss the future at the end of the season."
Allegri confirmed he would start the final with a back four, stating "two out of [Andrea] Barzagli, [Medhi] Benatia and [Daniele] Rugani will start at centre-back."
Mario Mandzukic, Mattia De Sciglio and Stefano Sturaro are all back in contention at the Stadio Olimpico as Juventus chase a fourth consecutive domestic double under Allegri.
"Winning the Coppa would be another great page in the story of Juventus," he added.
"We will face a team that can give us trouble from set pieces with very technical players, so we will have to be very focused and balanced.
"I expect the boys to give the fans, the club and me another great evening."