Tomori says he loves the idea of being part of the Rossoneri's history.
He told BBC Sport: "It's mad. You walk in every day and you see pictures of players like Maldini, (Franco) Baresi, Kaka, Zlatan (Ibrahimovic) and (Alessandro) Nesta.
"So you definitely feel the expectation knowing those players were in the same building.
"And it comes from the fans you meet in the city. You realise how much weight the shirt holds.
"I love that they're so proud of the club and there's an expectation for us to deliver and do what those before did."
On England coach Thomas Tuchel, Tomori says there's been contact ahead of the World Cup.
"I spoke to him after the last international break in November. We've spoken a few times and the message is to keep doing what I'm doing," Tomori says.
"The World Cup is six months away and there's a lot of football to be played.
"I know he's watching and keeping an eye because he called up (team-mate) Ruben Loftus-Cheek. That gives me the confidence I can make it.
"He came to Milan last season and I know he gets our data and sees our clips regularly too.
"The way he's spoken about it is that it's difficult because there's so many players in that position, and I get it because you have players like John Stones, Marc Guehi, Dan Burn and Ezri Konsa.
"But the World Cup is still a dream and I'm working towards that."