Di Vaio told a news conference in Italy that he would not return to his Italian Serie A club for 2013, and that Montreal's Major League Soccer expansion team was an interesting.
Montreal's technical director Nick De Santis said there's an offer on the table for the 35-year-old player, who plans to visit the city with his family at the end of May.
"I know that there are other offers on the table for him to pursue his career," De Santis told a media conference call. "I just hope that the next step, coming to Montreal, shows him that we are a club that are very serious in moving ourselves along as a professional club in North American soccer."
Should Di Vaio sign with Montreal, he would not be eligible to play in MLS until July since the transfer window is currently closed.
The Montreal offer is for a year and half, plus two more at the club's option.
Di Vaio, who leads Bologna with 10 goals, would give Montreal a third Italian player after forward Bernardo Corradi and defender Matteo Ferrari.
Di Vaio and Ferrari played together at Parma in the early 2000s.
De Santis noted Di Vaio had basically scored a goal every two games in recent season "in one of the toughest leagues in the world to score in."
He also said the Italian had "the mentality of a warrior," noting he has stayed with Bologna in recent years to help them fight relegation.
"He's been their main catalyst scoring important goals, leading this team, a young team, and he's got all the details and personality to help our team move along as well."
De Santis expressed confidence that Montreal had a shot at Di Vaio.
"When a player is willing to come in and see the city and meet the club and discussions we've had, we feel pretty positive," he said. "You never know at the last minute, that's why I told you we've spoken to other players as well to keep in consideration but of course Marco is one of them that we have a high interest in."