Westbrook, who finished fourth in Saturday's Heisman balloting, was arrested in 2012 and 2013 in incidents involving the mother of his two children, the Tulsa World reported.
The 23-year-old senior, who won the Biletnikoff Award last week as the nation's leading receiver, was not convicted following either arrest.
While school officials, including football coach Bob Stoops, declined comment on the arrests, the university released a statement to the newspaper on Sunday.
"The university conducts independent background checks on every entering student-athlete," the statement read. "While the university has declined to extend offers in other circumstances as a result of gathered information, nothing was reported in this case."
Westbrook is coming off a spectacular season in which he hauled in 74 catches for 1,465 yards and a school-record 16 touchdowns to help the Sooners (10-2) advance to a matchup against Auburn in the Sugar Bowl on Jan. 2.
Citing court documents and police reports, the newspaper reported that Westbrook was accused of throwing the woman to the ground in the first incident in August 2012.
The following year, she accused Westbrook of biting her arm and punching her in the face with a closed fist during an incident at her apartment in April 2013.
The Milam County District Attorney's office rejected charges against Westbrook in the first alleged attack, but filed misdemeanor family violence charges against him in the second innocent. Those charges were dropped when the accuser failed to show for a court appearance.
Oklahoma also released a statement from Westbrook in which he attempted to distance himself from the transgressions, saying they were behind him.
"There were some disagreements in the past that were cleared up years ago," Westbrook said. "We have resolved our issues and are focused on the future."