Multiple reports including Sky Sport Italia claim the deal is done after negotiations progressed rapidly today.
It will be a loan with obligation to buy for a total €16m plus bonuses, this format allowing Roma to spread the cost over two years, reaching €18-20m.
Genoa should also receive a percentage of any future transfer fee if Shomurodov were to move on from the Stadio Olimpico.
The Uzbekistan international only made his Serie A debut last season, impressing with eight goals and one assist in 31 top flight games, many of them off the bench.
He turned 26 last month and is primarily a centre-forward, although he can also share the spotlight with other strikers.
Genoa snapped him up from Russian club Rostov in October 2020 for €7.5m, so his transfer value has doubled in one year.
Shomurodov took a picture with coach Jose Mourinho in Moscow back in 2019 and Roma fans spotted it on his Instagram.
— Gianluca Di Marzio (@DiMarzio) July 28, 2021
— Alessandro Austini (@aleaus81) July 28, 2021