Kyrgios called Tomic the most hated athlete in Australia when the pair chatted about who the better player was on Instagram on Wednesday night.
Tomic, who won his only professional meeting in Kuyong in 2019, returned the service by offering to pay one million dollars for the one-on-one competition.
“At the end of the day, talk is cheap,” Tomic told the Sydney Morning Herald. “Whenever you want, I’m ready to do it 2-0. Put your money where your mouth is.
“Let the public decide who is better. I’ll beat you anywhere, anytime. If not, shut your mouth and go back to playing doubles.
“I will overtake you one by one,” he said. “In order not to make excuses, I’ll let you play on the grass whenever you want.
“You know what? Let’s settle this in the boxing ring. Put on your gloves, I’ll get over you there too. Let’s see who’s better once and for all.”
Kyrgios didn’t rule out a day-long boxing bout, but said the world number 418 will have to work to get back up the rankings to take the court with him.
“I’m still playing on tour, my brother. I have big fish to fry,” the world number 76er said in an Instagram video.
“If you want to play me and you want to set it straight, just come back to the top of the game. I’m here, I’m not going anywhere.”
Kyrgios won his first Grand Slam doubles title at the Australian Open this year and also reached the singles quarterfinals of the $8.5 million Indian Wells tournament.
One-time prodigy Tomic, who reached the Wimbledon quarterfinals as a teenager, recently lost in the first round of the $53,120 event in Mexico on the second-tier Challenger Tour.