The Ottawa native registered seven goals and 21 assists for 28 points in 42 games with the Dallas Stars and Vancouver Canucks this past season.
Several teams have also shown interest in Roy, including the Washington Capitals, St. Louis Blues, Calgary Flames and Winnipeg Jets.
The Ducks held talks with Roy's camp on Friday and are expected to reconnect today.
In 591 career NHL regular-season games with the Buffalo Sabres, Stars and Canucks, Roy has accumulated 168 goals and 287 assists for 455 points.
He was originally drafted by the Sabres in the second-round (32nd overall) of the 2001 NHL Entry Draft.