A person with knowledge of Cleveland's interest said the team is exploring the possibility of signing Oden, the former No. 1 overall pick whose NBA career has been sabotaged by injuries.
The Cavs are doing their due diligence while looking at Oden, said the person who spoke to The Associated Press on condition of anonymity Tuesday because the team's interest is contingent upon the center's health.
CBSSports.com first reported the Cavs and Miami Heat were leading the pursuit of Oden, who hasn't played since 2009 and has undergone three microfracture knee surgeries - two on his left knee.
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.
A defensive force during his one college season, the 7-foot Oden was the first player taken in the 2007 draft by Portland, who chose the soft-spoken big man over All-Star Kevin Durant. 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."