The pair will meet in the Wednesday night match on John Cain Arena, where Kokkinakis will take over the spotlight from his doubles partner Nick Kyrgios following his first-round exit.
Kokkinakis locked in a berth in the second round with a gutsy four-set win over Russian Roman Safiullin, while 15th seed Draper showed heart to overcome Argentine Mariano Navone in five sets, with both matches lasting more than four hours.
The South Australian was forced out of Brisbane with a hip injury, then Adelaide with a shoulder complaint, before suffering a leg injury early in the second set against Safiullin.
Meanwhile, back and hip issues mean Draper hasn't played since the Paris Masters in October, when he fell to another Australian, Alex de Minaur, in the round of 16.
Britain's Jack Draper is playing again after dealing with back and hip issues. (AP PHOTO)
However, he got the better of the world No.8 at the US Open, ending de Minaur's run in the quarter-finals, which was Draper's best performance in a grand slam.
"In the last month, I didn't play for maybe three weeks," 23-year-old Draper said.
"I was in a lot of pain with my back and my hip and it was a really difficult period for myself where I wasn't able to get any work for my body really as I wasn't able to play.
"It's a big spike in my (work) load obviously playing a four-hour match, but I think in all honesty, the best set I played was the last set and I felt the best in the last set as well, so that's a real positive.
"I think if I recover well, give myself another chance, I'll feel better in all areas."
The pair have met three times, with world No.18 Draper winning twice, but each meeting has gone down to the wire, including Great Britain's Davis Cup finals triumph in 2023.
"He's obviously a great player who had a very good year last year," 28-year-old Kokkinakis said.
"We've had three matches and he's won two, I've won one, all extremely tight matches.
"The first one I lost in Davis Cup, serving for the match, the next one I got him, and the last one was 7-5 in the third."
"It's going to be a battle for sure. Hopefully the body pulls up all right and I can give it my best."
AUSSIES IN ACTION ON DAY FOUR OF THE AUSTRALIAN OPEN ON WEDNESDAY:
Women's singles, second round:
Ajla Tomljanovic v 12-Diana Shnaider (RUS)
Talia Gibson v 11-Paula Badosa (ESP)
Men's singles, second round
Thanasi Kokkinakis v 15-Jack Draper (GBR)
Aleksandar Vukic v 22-Sebastian Korda (USA)
27-Jordan Thompson v Nuno Borges (POR)
James Duckworth v Roberto Carballes Baena (ESP)
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