The 34-year-old manager did not even last a season at Stamford Bridge. He was fired by the Blues in March after a run of poor results and rumors of player discontent.
However, during the 2010-11 season, AVB became the youngest manager ever to win a European competition when he guided FC Porto to the Europa League title.
Roma will hope the Portuguese manager can improve on their sides form this season.
The Italian side currently sit seventh in the table.
Current Roma manager Luis Enrique has been evasive in the past several weeks when questioned about his future at the club.
In a pre-match press conference this week, Enrique still wasn't telling, but did say that he'd made up his mind. (h/t Yahoo UK)
"There are only two possibilities: stay or go," the manager said. "I know 100-percent what I'm going to do, but I won't tell you. I haven't even told the team, otherwise the whole world would know a minute later."
A Bola says that Villas-Boas held secret meetings with Roma's general manager while he was still the manager at Chelsea.