The Cavs have not yet set up a visit with Roy, said the person who spoke on the condition of anonymity because the sides are only in preliminary discussions. Roy, a three-time All-Star, announced his retirement last season after five seasons with Portland because of chronic knee problems. After sitting out the lockout-condensed season, Roy wants to try and resume his once promising NBA career.
The Minnesota Timberwolves and other teams have also expressed an interest in Roy.
Roy and his representatives have spoken to members of the Chicago Bulls' staff as well, sources told ESPN.com. Yahoo! Sports reported on Saturday that the Bulls were one of four finalists for Roy's services.
Another source told the AP that the Golden State Warriors met with Roy earlier this week about joining the team.
The person, who spoke on condition of anonymity Tuesday because the talks were preliminary, also said the Warriors were hoping to meet with Roy again.
While he has only played for the Blazers, Golden State does offer some familiarity. Roy used to be represented by new Warriors general manager Bob Myers, a former sports agent.
The 27-year-old Roy averaged 19 points, 4.3 rebounds and 4.7 assists in 321 games. He was the No. 6 overall pick in the 2006 draft.
ESPNLosAngeles' Ramon Shelburne, ESPNChicago's Nick Friedell and The Associated Press contributed to this report.