There are several versions of the story, with Gianluca Di Marzio saying Roma offered €3m for a loan with a €15m obligation to buy, then a further €7m in bonuses.
Alfredo Pedulla reports an initial €24m fee with up to €4m to follow in add-ons.
Whatever the formula, it is a considerable sum for Milik, 26, considering he is out of contract next year.
Roma have offered Milik a five-year deal worth €5m-per-season, but he has yet to accept.
The Polish striker told Napoli to take him off the market recently and the Giallorossi must now convince him.
If Milik does move to the Italian capital, it could lead to the sale of Edin Dzeko.