The former Chelsea manager has managed the club previously. He spent three years in charge of Juventus before taking over as Italy boss in 2014, winning the league title each season with the Turin club.
Tottenham Hotspur manager Mauricio Pochettino is also well fancied by the oddsmakers. The Argentinian has impressed during his time in north London and has guided Spurs into the UEFA Champions League final and secured a fourth-place finish in the Premier League this season.
Odds (via Caesars)
Antonio Conte +150 (3-2)
Mauricio Pochettino +350 (7-2)
Maurizio Sarri +550 (11-2)
Simone Inzaghi +600 (6-1)
Jose Mourinho +700 (7-1)
Carlo Ancelotti +1200 (12-1)
Diego Simeone +1200 (12-1)
Conte has been out of work since being sacked by Chelsea last July after two years in charge.
The Italian won the Premier League in his first season and the FA Cup in his second, but the Blues only finished fifth in the league and missed out on UEFA Champions League qualification.
Conte has been linked with a Serie A return already this season. However, he has already ruled out replacing Claudio Ranieri at Roma in an interview with Gazzetta dello Sport (h/t Football Italia).
He has also been linked with a move to Inter Milan, and Tuttosport (h/t Calciomercato.com) says he has an agreement with the Nerazzurri.
Football writer David Amoyal expects Conte to head to the San Siro:
However, Conte moving to Juve is still a possibility, according to football writer Kaustubh Pandey:
Pochettino is also an option and has hinted recently he could be prised away from Tottenham if he were to lift the Champions League trophy with Spurs:
The 47-year-old has guided the club to their first-ever Champions League final, where they will take on Liverpool in Baku, Azerbaijan, on June 1.
Bleacher Report's Gianni Verschueren offered his view on Pochettino's chances of replacing Allegri:
Gianni Verschueren @ReverschPass
Pochettino has some flimsy connections to Piemonte and could consider his work at Spurs done if they win the Champions League. He has also hinted he's not happy with their transfer approach. I think the chances he ends up at Juventus are slim, but they certainly exist
Chelsea manager Maurizio Sarri, Lazio boss Simone Inzaghi and Jose Mourinho are also in contention, according to the oddsmakers.
Sarri has guided Chelsea to third place in the Premier League and into the finals of the Carabao Cup and Europa League in his first season in English football. However, he does not have the approval from some of the club's supporters who have called for him to be sacked throughout this season.
The 60-year-old has said he wants to stay at Stamford Bridge, but Chelsea will only decide his future after the Europa League final on May 29, according to Matt Law at The Telegraph.
Inzaghi has also impressed during his time in charge of Lazio and won the Coppa Italia on Wednesday with a 2-0 win over Atalanta.
ESPN FC's Matteo Bonetti explained why Inzaghi might be an option:
Whoever does take charge of Juventus will be tasked with maintaining their domestic dominance and bringing the Champions League trophy to Turin.
Allegri won the Serie A title five times and the Coppa Italia on four occasions, but he could not end the club's wait to be crowned European champions that stretches back to 1996.