Kyrgios and the Australian Olympic Committee have been at loggerheads over Rio since team chef de mission Kitty Chiller suggested the hotheaded 21-year-old and his Davis Cup team mate Bernard Tomic could miss out due to their on-court behaviour.
Tomic has since opted out of playing the Games, citing scheduling reasons, but Kyrgios remains in the selection frame despite the Chiller warning.
Kyrgios, who was backed by Tennis Australia on Friday as having made a "concerted effort" to improve his behaviour, posted an on-court photo of himself on his Facebook page and asked his followers whether they thought he should go to Rio.
"It's hard not to read all the stuff written about me... So I want your opinion," he wrote.
"Fiery passion and intense competitiveness to me are the things that represent the elite level of sport.
"If you think the Australian Olympic tennis team would be better without me then comment on this photo... BUT if you were the selector and you would want me out there battling for a medal LIKE and SHARE this picture."
Kyrgios has had several incidents of poor behaviour in the last 12 months and was given a suspended ban by the ATP last year for an off-colour comment directed at Swiss twice grand slam champion Stan Wawrinka.
He riled the Olympic team boss earlier this week by referring to her as "that Kitty Chiller" on his Twitter account, while adding: "If you don't want two of the best players in Australia to represent your country, so be it."
Chiller said his comments showed "maybe he doesn't really know what it means to be an Australian Olympian."
(Editing by Greg Stutchbury)
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