The full-back still has two years left on his contract with last season's treble-winners but has his heart set on a move after five seasons at Camp Nou.
"Roma have made a very tempting offer and Adriano feels it's time for a change," the defender's representative agent told Sport.
"Now is a good time to take on a new challenge and take advantage of the opportunity to play for a big Italian club like Roma.
"Adriano has a great relationship with everyone at Barcelona and they have behaved very well toward us.
"As professionals, the situation has to be managed with intelligence and patience in order to reach an agreement over a transfer."
The 30-year-old joined Barcelona from Sevilla in the summer of 2010 and has since made over 150 official appearances for the Catalans, winning La Liga four times and the Champions League twice in the process.