Osbourne was rushed to hospital few days ago after she collapsed due to a seizure at work.
The 28-year-old 'Fashion Police' host is currently in the hospital and is on anti-seizure medicines, reported TMZ online.
"The seizure was far more serious than first suspected. Doctors are running tests and we're told she'll be in the hospital for at least a few more days," a source said.
"We're told doctors say there's a real possibility that Kelly is an epileptic, but it's possible it was an isolated incident. If it's the latter, docs need to figure out what happened and how they can prevent another episode," it added.