The two sides face one another in Saint Petersburg on Tuesday, and the Rossoneri boss acknowledged that his team find themselves in a very competitive group.
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When asked about the man in charge of Zenit, former Roma boss Luciano Spalletti, Allegri had nothing but praise for his counterpart.
"Spalletti is showing he's a great trainer. He was close to winning the Scudetto with Roma and he has won the league title in Russia. He always gives a clear identity to his squads."
Milan midfielder Riccardo Montolivo, who was also present at the press conference, spoke of his excitement at being involved in Europe's premier club competition once again, having played in the tournament with Fiorentina two years ago.
"I am glad to be involved in the biggest club tournament again – to accept a new challenge and show my best," the midfielder said.
"Playing for the national team has brought me to a new level and with each match we look better. We are still finding our way, tactically, but I am sure we will find the best option – for me, and the team."