Kyrgios, who has come on leaps and bounds in the last 18 months, became the first Australian to reach the quarter-finals in Melbourne for 10 years.
The clash could raise the roof on Rod Laver Arena, which has been scheduled to start at around 8:30am (GMT), and the British No 1 will be set on improving his perfect 10-0 record against Australian players at tour level.
But Kyrgios has a tendency to cause an upset or two, having beaten then world No 1 Rafael Nadal in the fourth round at Wimbledon last year.
The 19-year-old had saved a match point as he came from two sets down to beat Roger Federer’s conqueror Andreas Seppi 8-6 in the fifth set of an epic clash to become the first Australian man to reach the quarter-finals since Lleyton Hewitt in 2005.
Murray secured another last eight appearance on Sunday with a rollercoaster victory over Grigor Dimitrov.
The Scot missed the 2013 French Open but has now reached the quarter-final stage at the last 16 slams he has contested.
Sixth seed Murray has dropped just one set in the tournament so far, but the proud Greek-Malaysian Australian is improving with every major tournament and climbing the rankings at a speed of knots – he is currently ranked world No 53.
He will be supported by a partisan and expectant home crowd as the pair meet for only the second time with the Scot winning in straight sets in Toronto last summer.
“Obviously the crowd will be right behind him. Understandably so,” said Murray, who is on course to meet Rafael Nadal in the semi-finals and Novak Djokovic in the final.
“That’s just something that I’ll have to deal with in my way. I’ve played a lot of matches.
“I’ve played in the French Open against French players where the crowd can be very difficult. I’ve experienced it before, so hopefully I’ll deal with it well.”
The talented Krygios has developed a reputation for his audacious shots and for his crowd interaction – he asked a couple leaving his fourth-round match “where are you going?” when they stood up in the stands. “I definitely believe that I can do it,” he said.
Former Wimbledon champion Murray bristled at suggestions he might disappoint the Australian crowd if he beats the local hope. “I plan on trying to beat Nick. I’m not planning on trying to break anybody’s hearts,” Murray says. “This is tennis. This is sport.”
Third seed Nadal or seventh seed Tomas Berdych will await the winner in the semi-final.
The 14-time Grand Slam champion has an 18-3 career record against Czech star Berdych, who won three of their first four meetings but has lost the last 17 in a row.