Marks, who cited three unnamed sources, revealed the report on The Russillo Show (starting at the 41-minute mark).
The 30-year-old Bogdanovic, who averaged a career-high 18.0 points on 49.7 percent shooting (42.5 percent from three-point range) for the Indiana Pacers, is a free agent this summer.
The Spurs were the NBA's No. 1 three-point shooting team at 39.2 percent last season, and adding Bogdanovic would only solidify the team's strength.
The issue is whether the Spurs can afford him.
Bogdanovic, coming of a two-year, $21 million deal with Indiana, figures to get paid handsomely this summer after registering career-best offensive marks.
San Antonio already has more than $100 million committed to its 2019-20 payroll, per HoopsHype, and 17 NBA teams have more salary-cap space next season.
The NBA cap is set at $109 million, per Shams Charania of The Athletic and Stadium, so the Spurs would have to shed some money to make a Bogdanovic deal work.
If San Antonio can make it happen, though, then the Spurs could have one of the better wing-scoring combos in the league with Bogdanovic and DeMar DeRozan.
DeRozan, who came to San Antonio via a trade with the Toronto Raptors last offseason, averaged 21.2 points on 48.1 percent shooting last season.
DeRozan and LaMarcus Aldridge were the only two Spurs to score 14 or more points per game last year, so the team could use a tertiary scorer to help take some of the offensive burden off them. Bogdanovic would fit that bill, but the question is whether San Antonio could make it work.