Unsung Sydneysider Aleksandar Vukic has set his sights on a Davis Cup call-up after a breakout performance at the Australian Open.

Alex de Minaur is the last home player left in the singles after the Vukic had his chances at a maiden fourth-round grand slam berth but couldn't quite put away British 15th seed Draper, losing 6-4 2-6 5-7 7-6 (7-5) 7-6 (10-8).

Both coming off five-set wins in their first two rounds, Vukic and Draper traded blows for three hours and 58 minutes in a nail-biting Friday night tussle on Margaret Court Arena.

A match tiebreak was needed to separate the pair, with 23-year-old Draper clinching the decider with an unreturnable serve at 12.55am local time.

"I thought he was done and he just came back from the dead," said Draper, who had been leading world No.68 Vukic 3-1 in the deciding set.

"He was playing incredible."

An admittedly "buggered" Vukic, 28, described the result as bittersweet and nothing to be ashamed of.

"I left it all out there," he told reporters.

"Jack's an incredible competitor who I have a lot of respect for. Unfortunately, one of us had to win.

"It's one of those that I'll take a lot of confidence from moving forward for the rest of the year."

Vukic, who ended last season with wins over top-20 players Casper Ruud and Frances Tiafoe, signalled he would put his hand up for Davis Cup duties.

But he confirmed he's not received any communication from Cup captain Lleyton Hewitt following injuries to Nick Kyrgios and Thanasi Kokkinakis, who were nominated for Australia's qualifying tie against Sweden in Stockholm at the end of the month.

"Representing Australia would be such a privilege," Vukic said.

"I want to accomplish as much as I can.

"Whether that's going deep in a slam, representing Davis Cup, going deep in Masters, I want to push whatever I can."

It was Vukic's first time in the pressure-cooker environment of a slam third round, having already spent more than six hours on court after five-setters against No.22 seed Sebastian Korda and Bosnian Damir Dzumhur.

He would have joined Hewitt, de Minaur, Kyrgios and Bernard Tomic as the only Australian men to make the fourth round of the Open in the past two decades with a win, but fell agonisingly short.

Draper is fast becoming a grand-slam spoiler for Australians, knocking de Minaur out of last year's US Open quarter-finals and downing Kokkinakis in a marathon five-setter in the last round.

His prize is a date with world No.3 and four-time grand slam champion Carlos Alcaraz, who he beat on grass at Queen's Club last year, for a spot in the quarter-finals in Melbourne.

"My body doesn't feel too great, lucky I've got a good physio," said the 2024 US Open semi-finalist.

"I'm just thinking about my recovery and getting off the court. I don't want to think about that (playing Alcaraz) yet.

"Carlos is a special talent, an unbelievable player and someone I have a good friendship with, so I think that's going to be incredible match ... I'll give it my all."