The Italian previously indicated his next job will be away from his homeland and, along with former Barcelona coach Luis Enrique, he is reportedly a frontrunner to succeed Arsene Wenger at the Emirates Stadium.
Arsenal want to make an appointment before the World Cup kicks off on June 14, but are also acutely aware of the distraction of the finals in Russian Federation, a shorter transfer window that closes on August 9 and their pre-season plans, which mean that in an ideal world it would be done quicker. "We will talk about the future after the end of the season, we want him to stay, I am sure there is a bright future ahead of us".
Before his arrival, no Italian club had ever achieved back-to-back doubles, while the last time Juventus had won the league and cup in the same season was in 1995.
Chelsea, who are expected to replace Antonio Conte after the FA Cup final later this month, are also interested in Allegri and could yet rival Arsenal, who have not qualified for next season's Champions League.
Juventus manager Massimiliano Allegri is now one of the frontrunners to take over at either Arsenal or Chelsea at the end of this season.
"It will be necessary to have the clarity to understand how to improve ourselves, to win back-to-back is always hard and we must always build to try to win on all fronts".
Allegri has taken Juventus to another level.
The Juventus boss led his side to a 4-0 win in the Coppa Italia final last night and have effectively secured the Serie A title.
Defender Andrea Barzagli is similarly unprepared to rest on his laurels with two games of the league season remaining. "Which competitive club can give him that opportunity now?"
"He knows he needs a fresh experience, but he's not the guy who wants to go to England without a real chance to win", a friend told Yahoo Sport.