A Raiders source told Mathai that the Raiders playing on the other side of San Francisco Bay for one season is a "distinct possibility."
Owner Mark Davis is moving the Raiders in 2020 to Las Vegas, where a new stadium is being built, and the City of Oakland recently sued the Raiders and the rest of the NFL over the move.
That prompted Davis to opt out of a contract to have the Raiders play one more season in Oakland.
However, there are questions about the San Francisco plan.
NFL Network's Ian Rapoport, according to unnamed sources, said the Raiders can't unilaterally move to San Francisco because it falls within the San Francisco 49ers' territorial market.
That means the 49ers might try to block the move, which might mean the NFL could tell the 49ers to let the Raiders play in San Francisco or at Levi's Stadium.
There also has been speculation that the Raiders might share Levi's Stadium in Santa Clara with the 49ers next season.
The Raiders played in San Francisco during their first two seasons, 1960 and 1961, at Kezar Stadium and Candlestick Park, before Frank Youell Field and then the Oakland-Alameda County Coliseum were built in Oakland.