Shevchenko spent seven seasons at the San Siro from 1999-2006, scoring 127 league goals, and was in north Italy for the unveiling of the club's new Casa Milan headquarters on Monday.
A museum, a merchandise outlet, a square with a big screen and a restaurant are some of the Casa Milan's attractions.
And Shevchenko hoped it could also open a new chapter for Milan, who struggled into eighth spot in the 2013-14 season.
"It's nice to come back to Milan," Shevchenko told Milan Channel.
"This new base is great. I had some excellent years here in this city.
"The team didn't have a great season but now it's finished. The club needs to look forward and I am sure that (Adriano) Galliani and the president (Silvio Berlusconi) will do special things.
"I hope that Milan can become one of the big players in Italy and in Europe again."
Both Galliani and Shevchenko threw their support behind Brazilian Kaka remaining with the club.
"I've seen Kaka reborn, it's been difficult even for him this season but Ricky has played very well. We fans hope that he stays," the Ukrainian said.
On coach Clarence Seedorf, Shevchenko said the former midfield maestro at the San Siro deserved to keep his job.
"The club will decide soon about Seedorf," he said.
"I think that it's always difficult for a coach at the beginning but Clarence has done everything possible and he has done well.
"In some ways he has done extremely well."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.