The former Inter Milan forward is ready to return to Italy after rebuilding his career in Brazil for the past 18 months.
Globoesporte says that he told his friends: "Roma have an offer to make me."
Adriano's contract runs out on May 31, making him an attractive free agent for a cash-strapped club like Roma.
However, Flamengo don't want to lose him.
"If he wants to stay, we'll find a way to resolve the financial problem," Flamengo President Patricia Amerim said.