The Giallorossi have been in talks to land the Polish striker for several days, but he wasn’t entirely convinced of a move to the Italian capital.
However Sky Sport Italia reports Milik’s agent met with Roma directors at their Trigoria training ground on Thursday and a deal is all but complete.
The striker will reportedly join the Giallorossi on loan with an obligation to buy for a fee of €18 million plus €7m in bonuses.
Since Milik will not join Roma outright he must first extend his contract with Napoli, which runs until June 2022, for a deal to be completed.
The move also means that Dzeko is on his way out of the capital, with Juventus ready to welcome the striker.
It’s believed the Old Lady and Roma already have a deal in place for €15m, while the 34-year-old will earn €7.5m a season plus bonuses.
Reports suggest Juve have pushed to close a deal for Dzeko at the request of coach Andrea Pirlo, which means they may pull out of the race to sign Luis Suarez from Barcelona.