Sullinger, who is projected to be a lottery pick in the draft on June 28, underwent a series of medical tests at the draft combine a week ago. A number of NBA team doctors have reviewed the information from the NBA and have told their front office staff that Sullinger's back issues could shorten his NBA career, and some have advised their teams not to draft him in the first round.
Sullinger's agent, David Falk, told ESPN.com by phone that he was not in a position to comment on the story.
Sullinger's father, Satch Sullinger, said he believes the issue isn't that serious.
"He had a bulging area that was due to his hamstring and quads being so tight," Satch Sullinger told ESPN.com senior college basketball writer Andy Katz in a phone call Monday afternoon. "It pulled on his hip flexor and he's been taking care of it to loosen it. You can call it a red flag if you want. But it's tight hamstring and tight quads. He's been to doctors, he's doing yoga and deep tissue massage. The flexibility is helping take the pressure off the area.
"We've got nothing to hide. At this stage it's all about what they can't do. Jared is a skilled player. A two-time All-American. He can play."
Ohio State coach Thad Matta told Katz by text message Monday: "Jared is fine. He's moving better than I've ever seen him move."
ESPN.com currently has Sullinger, who who missed two games for Ohio State in early December with back spasms, slated to go No. 10 in Mock Draft 7.0. However, such news may cause Sullinger to free fall in next week's draft.
In 2009, Pittsburgh's DeJuan Blair was also red flagged by the NBA when medical tests at the NBA combine revealed he didn't have ACL's in either knee. At the time Blair was projected as a late lottery pick. He slid all the way out of the first round.
Sullinger worked out in New Orleans on Monday. He also previously worked out for Golden State and Portland. He's scheduled to meet with Toronto (Thursday), Cleveland (Friday) and Detroit (June 26).
Sullinger has received lukewarm reviews of his predraft agility tests.
"I'm not a testing type of guy. I'm a basketball player," Sullinger said Monday in New Orleans. "If I'm so robotic in testing or I couldn't do the testing because I wasn't robotic enough, I apologize to everybody that thinks I didn't do well. That's just me. I'm a basketball player. I know how to play with a basketball."
Information from The Associated Press was used in this report.