The deal is for the veteran's minimum of $1.448 million, according to the report.
Bonner, 34, averaged 3.2 points, 2.1 rebounds and a career-low 11.3 minutes per contest in 61 games in the regular season for the Spurs, who won their fifth NBA championship in franchise history.
Of the 14 Spurs that saw action last season, 13 are signed for the 2014-15 season.
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In 10 NBA seasons, Bonner has averaged 6.2 points and 3.2 rebounds per game.
- Scooby Axson