Bonucci, 30, arrived in Milan to ahead of a £36.9million move from Juventus today.
And Italian journalist Palmeri believes the deal has already been finalised.
He tweeted this afternoon: “DONE! Bonucci to Milan for 40m€!”
Reports in Italy claim Bonucci will sign a five-year deal and will earn £110,000 a week after tax.
Chelsea and Manchester City showed an interest in Bonucci last summer but he stayed in Italy for personal reasons.
The fee is huge for a 30-year-old who, realistically, will have little sell-on value by the time his contract is up aged 35.
But Bonucci is considered one of the best defenders on the planet and boss Vincenzo Montella wants him to shore up a defence that leaked 45 goals last season.
The Italy international leaves Juve having played 300 games since signing from Bari in August 2010.
