CBSSports.com, citing a source, reports Oden hopes to meet with Heat officials within the next week.
The Cavaliers are doing their due diligence while evaluating Oden, said a person who spoke to The Associated Press on condition of anonymity because the team's interest is contingent upon the center's health.
ESPN.com reported on Jan. 10 that Oden was considering a comeback, but not before the 2013-14 season. Sources told ESPN.com that multiple teams had expressed interest in signing oden to a multiyear deal that would allow him to continue his rehab until he can get back on the court in the fall.
A day later, ESPNDallas.com reported that the Dallas Mavericks were among the teams interested in Oden as well.
Before watching No. 11 Ohio State's 58-49 win over Wisconsin on Tuesday night in Columbus, Ohio, Oden said he hopes to be healthy enough to take another shot at pro ball.
"I don't know when, but I'm taking this year off. I'll play next year," said Oden, who led the Buckeyes to the Final Four as a freshman in 2007.
Oden's agent, Mike Conley Sr., could not be reached for comment.
Boston Celtics president of basketball operations Danny Ainge confirmed on Jan. 17 the team was "monitoring" Oden, but said it hasn't made an attempt to sign the 7-footer.
CBSSports.com reported the Celtics have expressed interest in Oden, but that the former Ohio State star prefers either Miami or Cleveland.
Oden was limited to just 82 games with the Trail Blazers, averaging 9.2 points and 7.3 rebounds. Oden has not played since 2009, and he had his last operation on Feb. 20 last year.
Portland waived Oden last March, ending a troubled five-year run with a player who entered the league with superstar potential.
Any team that signs the 25-year-old Oden would be taking a risk. But for a rebuilding team like the Cavs, who are looking to add pieces around All-Star point guard Kyrie Irving, the possibility Oden could develop into a productive player is enticing.
Oden said he has no preference on which team he plays for.
"Right now, I'm not worrying about where," he said. "I'm only worried about my knee."
Information from The Associated Press and ESPNBoston.com's Greg Payne was used in this report.