Allegri won the 2011 Serie A title in his first year in charge at San Siro and looks set to dump the Gunners out of Europe after Milan won 4-0 in the first leg of their Champions League last-16 tie.
Speaking ahead of the match, Allegri defended Wenger as a manager but said the Arsenal boss needed to make marquee signings as a statement of the club's ambition to both players and fans.
"For me it's impossible to win the title or Champions League without signing big players," Allegri told The Sun. "You will never do it without big players. That goes for Arsenal, Milan or any big club. You must buy big."
Allegri took charge of Milan side that signed the likes of Robinho, Zlatan Ibrahimovic, Kevin-Prince Boateng and Antonio Cassano and delivered instant success, winning their first Scudetto since 2004.
"I have a strong team but in that I have three big players, bringing experience, character, technical ability and leadership. You need leaders," he added. "For me in every team there are two leaders. One technical and tactical leader and one with character.
Allegri, who is well placed to win the Italian title once again this season, has sympathy for the approach of his opposite number but believes the club's policy of selling off their star names needs to change.
"It's not fair to criticise Wenger so much and it is not right, because every year Arsenal sell one big player or two big players and the team still manage to play well and finish in the top four.
"But it's also true that if they want to win trophies they have to keep their best players. And make two or three big signings.
"If somebody told me this summer we have to sell Zlatan and Prince I would say no. No. Noooo..."
Milan currently lead Serie A, three points ahead of Juventus, and have one foot in the quarter-finals of the Champions League.