The veteran forward signed his contract on Friday.
"I accepted to stay only because, as always, I feel I can still be useful and competitive," he told the Corriere dello Sport.
"I will be the one to decide when I retire. I need one goal to be the top scorer in European competition, three to equal Marco Van Basten's tally with Milan and seven to reach Roberto Baggio in the all-time record of Italian marksmen.
"I feel that this next year will be the one to achieve this incredible hat-trick of records."