Professional tennis players from Russia and Belarus were banned from Wimbledon in 2022 as the nations continued their invasion of Ukraine.
While men's and women's players are back permitted to play on the ATP and WTA tours, they can only do so without representing Russia or Belarus.
Kokkinakis defied advice from Tennis Australia not to compete in a lucrative exhibition tournament in Russia.
Few athletes from Western nations have ventured to Russia since the war began almost three years ago, with the country all but cast out of the international sporting arena.
But the Sydney Morning Herald is reporting Kokkinakis defied backed advice from TA not to play in an exhibition in St Petersburg run by a state-owned energy company blacklisted by the federal government following Vladimir Putin's invasion of Ukraine.
The exhibition from November 29 to December 1 reportedly included current and former Russian players as well as seven internationals, including Kokkinakis and Spanish former Wimbledon semi-finalist Roberto Bautista Agut.
The event's major sponsor was state-owned Russian gas and oil giant Gazprom, which has reportedly been the subject of financial sanctions imposed by Australia's Department of Foreign Affairs and Trade since April 2022.
Kokkinakis's management did not immediately respond to a request for comment but TA delivered a statement warning Australians not to play in Russia.
"For several years, Tennis Australia has publicly and privately supported Ukraine athletes and sought and abided by federal government policy and recommendations in regard to Russia. This support and compliance continues," the statement said.
"We advise athletes against competing in Russia and are in ongoing discussions with DFAT to provide education to players about the potential ramifications for doing business in this area."
Doubles great Todd Woodbridge criticised Kokkinakis during this month's Australian Open for pulling out of the Adelaide International after playing a pre-summer exhibition tournament.
But the injury-plagued 28-year-old said he was just "trying to make a living" just like Woodbridge - a tennis commentator and game show host for Nine - after being sidelined for much of his stop-start career.
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