Adriano's agent expects the Brazilian to complete his move to Roma in the next few days.
The former Inter Milan striker has rediscovered his form and hunger for football since returning to his homeland to join Flamengo last summer.
He recently indicated his desire to come back to Italy and confirmed last week that negotiations were taking place with Roma following the expiration of his Flamengo deal.
The 28-year-old's representative Gilmar Rinaldi now believes the transfer will be finalised by Wednesday at the latest.
"Adriano should be at Roma on June 8 or at the latest June 9," he told VoceGiallorossa.it.
"We are still evaluating some things."