Roma are hoping that Adriano will agree to a mutual termination of his contract, according to La Gazzetta dello Sport.
The 29-year-old Brazilian striker has disappointed Roma since his arrival from Flamengo on a free transfer last summer.
Adriano currently earns €5m a season before tax and his existing deal isn't due to expire until 2013.
Roma would like to make a saving of €10m on his wages by severing their ties with the player as soon as possible.
La Gazzetta understands Adriano will be allowed to recover his fitness at Trigoria then move back to Brazil either with Flamengo or Corinthians.