The claim came as Odom continued to fight for his life after being found unresponsive at the Love Ranch in Crystal Nevada on Tuesday afternoon.
Officials from the Nye County Sheriff's Office said that Odom's blood had been taken by investigators and was being processed.
When rescuers arrived, he was "unconscious but breathing," Sheriff Sharon Wehrly said. "He had blood coming from his nose and mouth along with a white substance."
According to police, a 911 caller reported around 3:15 p.m. that he had used cocaine on Saturday, but it was unclear if the use had continued into the weekend.
Police said the caller also reported that he had taken up to 10 tabs of sexual enhancement drugs over the past three days. It was not clear which specific drug the caller was referring to.
A helicopter landed at 4:37 p.m. to take Odom to the hospital, but he couldn't fit on the aircraft. Accompanied by a nurse, he arrived at the hospital at 5:30 p.m. Officials said his level of care was not diminished.
Reps for Odom did not immediately respond to a request for comment.
Odom, 35, had been staying at the Love Ranch in Crystal, Nevada for a few days before his hospitalization Tuesday. After receiving treatment at Pahrump's Desert View Hospital, he was transferred to another hospital in Las Vegas, where he remains.