Reports suggest Pato is unsettled at the San Siro and the Brazil international has been heavily linked with a return to his homeland.
Rossoneri vice-president Adriano Galliani revealed earlier this week the Serie A giants had received an offer from an unnamed club for the 23-year-old.
Gobbi has now confirmed Corinthians have entered "early talks" over signing the frontman.
He told Lancenet: "We sounded him out, there is interest, but we have to keep calm. I can't comment on what Milan said.
"This kind of subject affects the fans, we have to go slowly. And if the negotiations do happen, then great."
Gobbi added: "It's still very early talks. It's like dating a woman, you sound her out first, see where she lives, get her phone number, talk with her friends, find out what she likes, check if there is interest, then you invite her for dinner. Then schedule other dinners to have success.
"Only then you start dating her, then you get engaged and married. Everything takes its own time."