"I am convinced that, with a full squad, we are on par with Real Madrid," Allegri told La Stampa.
"The only exception is Barcelona."
The Italian tactician is clearly in confident mood following the Rossoneri's Serie A title triumph, although Milan's shortcomings in the UEFA Champions League last season means Allegri's side still have something to prove.
Milan failed to successfully navigate the round of 16 in Europe after they fell to Barclays Premier League side Tottenham Hotspur.
"We went out against Tottenham because of some ill luck and a full infirmary," Allegri said.
"I do not have to build a team, but I have to improve it. AC Milan are not perfect, if perfection is something that exists. Let me give you an example: when Barcelona lose the ball, they try to regain possession at a frenetic pace. That is one aspect we have to improve."
Milan are looking to bolster their midfield with the arrival of Alberto Aquilani after failing to lure Fiorentina's Riccardo Montolivo to the San Siro.