The 44-year-old stated that the big Swede is among the world's three best players at the moment, and took time to praise his team and the board who helped put the side together
Speaking at the press conference ahead of the second-leg clash with Arsenal in the round of 16 of the Champions League on Tuesday, the trainer praised the striker and warned against complacency, following the 4-0 win over the Gunners at San Siro in the first game.
"Tomorrow may seem like an easy game, but only in appearance. In reality it is not. We must have great concentration, we must not underestimate the game.
"We have a great opportunity to reach the quarter-finals and we will do everything we can to get there.
"Ibrahimovic? Hopefully he will win the Ballon d'Or, although much will depend on the results that we achieve this year.
"Along with Messi and Cristiano Ronaldo, the three of them are at this moment the best players in the world."
Allegri reserved special praise for the management of the club, stating that the excellent results in the transfer market have been the catalyst behind AC Milan's success.
"In any case this is not Ibrahimovic or Allegri's Milan, Milan has been built by the club that in a year and half have brought in Ibrahimovic, Robinho, Boateng, 20 players in total.
"And in this year and a half, thanks to this, we have won the Scudetto, the Italian Super Cup and now we are fighting on all three fronts."