The 16-year-old right-back has never figured in the first-team squad of the Serie B side but impressed United's scouts during an international youth team event last year, where he was voted player of the tournament.
"When they called me, I really couldn't believe it," he told Gazzetta dello Sport. "I didn't believe that it was really him (Sir Alex Ferguson) on the phone."
Reports suggest Massacci has already spent three days in Manchester, having a medical, and is set to fly back on Sunday to sign on the dotted line, and the teenager admits he has been left somewhat stunned by it all.
He added: "It was him (Ferguson), and I had an hour-long chat with him, in English. He seemed to me a modest, simple, incredible person.
"Nobody, not him, nor the whole atmosphere, made the pressure of who they are and what they represent in footballing history weigh on my shoulders."
He added: "In life a chance like this only comes past you once, and you've got to grab it with both hands.
"Even if at 16 years old it isn't an easy decision, you have to leave your home, family and friends. But I don't want to have regrets."
It is not the first time Ferguson and United have raided Italian youth teams, having previously snapped up Giuseppe Rossi and Federico Macheda.
Massacci becomes United's third signing of the summer, after shelling out £15million on Antonio Valencia and bringing in free agent Michael Owen.