Speaking to Sky Sports, De Zerbi said: "We feel we can write another part of Brighton's history.
"When I hear that big teams are interested in me it is an honour. I am proud, but my focus is on my work day-by-day.
"I would like in my career to compete to win the Premier League, Serie A, Bundesliga, La Liga, Champions League but there isn't a time when you have to go and compete, or to wait some more time.
"Milan for me is not a normal club because as a player I was born in AC Milan. For my life I will always be grateful for Milan.
"I love my country, I love Italy, I love Italian football. For sure one of my targets is to go back and work in my country, but I don't know when is the time."