Lynch was arrested by the California Highway Patrol on Interstate 880 and taken to Santa Rita Jail, where he was cited and released, the newspaper reported.
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A CHP spokesman told the Mercury News that Lynch submitted to a blood test after he was in custody. Lynch was found to be over the .08 legal limit, although no specific number was given.
Calls to the Alameda County Sheriff's department by NFL.com and NFL Network on Monday were unsuccessful.
UPDATE: An Alameda County District Attorney spokeswoman told NFL.com and NFL Network on Tuesday that Lynch is scheduled to appear Aug. 14 in Wiley W. Manuel Courthouse in Oakland.
"The DA will review the CHP reports and make a charging determination (before the scheduled court date)," the spokeswoman said.
In a statement to The Associated Press, the Seahawks said, "We are aware of the situation with Marshawn and still gathering information."
Lynch, a former star running back at the University of California, previously had his license revoked in 2008 for failure to exercise due care toward a pedestrian after he hit a 27-year-old woman and kept driving. In 2009, Lynch was suspended for three games after pleading guilty to a misdemeanor gun charge.