The newspaper said Turner will replace Mike McCarthy, who guided the 49ers to the NFL's worst offense in 2005. McCarthy was named head coach of the Green Bay Packers last week.
Turner was fired as head coach of the Oakland Raiders earlier this month. He coached the Raiders to a disappointing 4-12 record this season, despite having a multi-talented roster.
Turner, 53, was head coach in Washington for seven seasons, where he tallied a record of 49-59-1. He led the Redskins to an NFC East title in 1999, but was fired 13 games into the 2000 campaign.