Anderson is Bonds' former personal trainer.
The Times report said federal authorities are considering criminal charges against Anderson's wife, Nicole Gestas, his mother-in-law, Madeleine Gestas.
Earlier this summer, the newspaper reported that a federal "target letter" to Anderson's wife, dated last November, said authorities shifted their focus to Madeline Gestas' taxes.
She is a California businesswoman who previously has been subject to tax liens.
"There are violations that both Nicole and Madeleine are worried about," Nicole Gestas' attorney, Charles J. Smith of Redwood City, Calif., told the Times in a telephone interview Friday. "They are matters that I don't believe would rise to the level they would prosecute under the current standards of the U.S. attorney's office."
Bonds has denied the charges and Anderson has vowed never to testify.