Australia's Chef de Mission Kitty Chiller said the incident was a "light warning" and that she had written to the Rio organising committee and mayor demanding action.
"Obviously you can't ignore that stuff. We have got some stuff together with our family to make sure they are looked after," Mills, who plays for San Antonio Spurs in the NBA, told News Corp.
"It is an Olympics and you want to make sure you share that experience with your family and friends as much as you can.
"Definitely I am putting some focus into that to make sure they are looked after and healthy."
Asked if he would take a bodyguard to Rio, Mills said: "Yeah, over in America we have got some people connected to make sure they are looked after."
(Reporting by Ian Rodricks in Bengaluru; editing by Sudipto Ganguly)
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