The Serie A side has held talks with Manchester United football director John Murtough over a possible deal to sign striker Rasmus Hojlund, with the loan of Greenwood also discussed.
United are believed to be open to loaning Greenwood with boss Erik ten Hag preferring not to sell the 21-year-old.
However, the Red Devils have not yet made a final decision on whether or not to let Greenwood leave for the Italian side.
The forward is contracted to Manchester United until 2025 and the club have the option of an additional year.
In February, Greater Manchester Police stated Greenwood 'no longer faces criminal proceedings'.
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The forward had been charged with attempted rape, engaging in controlling and coercive behaviour and assault.
However, the Crown Prosecution Service later dropped all charges against the player, with United conducting their own process.
United have been unsure on what course of action to take over Greenwood over the past few months but expect to find a final outcome before the start of the season.
Greenwood joined Manchester United aged six and progressed through the academy ranks at the club.
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He finished as top scorer of the U18 Premier League North with 17 goals in 21 games in the 2017/18 season before making his full debut against Paris Saint-Germain in March 2019.
Greenwood has not featured for United since the 1-0 win against West Ham in January 2022.