The coach of the Serie A champions believes his side are only outdone by Barcelona, while stating that Aquilani will add quality to the team
After unseating Inter in Serie A last season, Milan are hoping to mount a serious challenge in the Champions League while also retaining their league crown.
Milan failed to go beyond the Round of 16 in the Uefa competition in the 2010-11 campaign, but Allegri thinks that Barcelona are the only club capable of posing a threat to his side.
"We went out against Tottenham because of some ill luck and a full infirmary," Allegri told La Stampa.
"I am convinced that, with a full squad, we are on par with Real Madrid. The only exception is Barcelona."
The Italian coach, who assumed the reins of Milan last summer, admits there is work to be done on his side and sets the Catalan club as a role model for the team.
"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," Allegri added.
"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."
Questioned about Alberto Aquilani, who is close to joining the club from Liverpool, Allegri stated he has no clue why the player was not signed by Juventus after playing for the Turin-based club last season on loan.
"Aquilani did not play poorly for Juventus: I do not know if they did not sign him because of cash issues or any other kind," he conceded.
"We scoured Italy and Europe and we are convinced he will be an asset."
The champions begin their league title defence away to Cagliari on Saturday, kicking-off at 20:45 CET with full coverage on Goal.com.