The man told sheriff's deputies at least three men assaulted him but Randolph was not among them. No arrests have been made, and authorities said none were expected on Monday.
Police identified the victim as 26-year-old James Beasley of Portland.
Clackamas County Sheriff's Sgt. James Rhodes said Randolph was in his home outside Portland when the beating occurred early Saturday. Beasley was treated for head and face injuries and released from a hospital later that afternoon, when he called police, Rhodes said.
Officers served a search warrant early Sunday. They spoke with 10 people in the home at the time and recovered pool cues and blood evidence. They did not find drugs in the home.
Rhodes said the evidence "was consistent with the victim's statement about where and how he was assaulted," and authorities were trying to figure out who was involved in the assault.
The victim told officers that he recognized Randolph and was certain he wasn't involved in the beating, but he didn't know the names of the people who assaulted him. The victim said there were about 20 people at Randolph's home at the time.
Rhodes said detectives will probably ask Beasley to pick the suspects from a line up.
Randolph has not spoken to the officers based on the advice of his lawyer, Rhodes said. He didn't know the lawyer's name.
Attempts to reach Randolph have been unsuccessful. Nobody answered the intercom system at his gated home in West Linn on Monday. Two sport-utility vehicles drove away, and their occupants did not stop to speak with a reporter from The Associated Press.
The Grizzlies declined to comment.
There was no listed phone number for Beasley.
Randolph averaged 20 points and 12 rebounds per game with Memphis last season. He was drafted in 2001 by the Portland Trail Blazers and played there six seasons before being traded to New York. He was later traded to the Los Angeles Clippers, then to Memphis in 2009.
The Grizzlies signed Randolph to a four-year contract extension in April during the first-round of the playoffs. He became only their second All-Star during the 2009-10 season.
Randolph's past troubles also have included an arrest for driving under the influence of intoxicants after a police officer said he smelled marijuana in Randolph's car and a practice fight in which he broke former teammate Ruben Patterson's eye socket.
In 2009, he was suspended for two games for punching a Phoenix Suns player.