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Edmund, ranked 49, is the only British man in this year's field after five-time finalist Murray's injury withdrawal before the tournament.
The introverted 23-year-old Yorkshireman is only the fourth British man to get this far in Melbourne following his upset of world No.3 Grigor Dimitrov in the quarters.
He has kept a lid on his expectations during his mind-whirring charge through the field, but has impressed with his penetrative serve and booming forehand during his giant-killing run.
"I don't think about I'm going to win it. I think the next match is in my head. I believe I can win that, like the last one and every match," Edmund said.
"I've gone in there knowing where my game is at, knowing what I want to do on court, not taking anything for granted.
"I go in there, do what I need to do, play my game as best as I can, then move on to the next one. Match by match, that's key for me really, not thinking too far ahead."
But Edmund dropped his inscrutable guard when he described his feelings of reaching the last four at a Grand Slam after mastering Dimitrov.
"I am loving it right now, just the way I'm playing," he said.
"I'm 23 years old, my first Grand Slam semi-final. For the first time I played on one of the biggest courts in the world and to beat a quality of player like Grigor.
"They're great feelings. You don't obviously play in the semi-finals of a Grand Slam every day."
He will fancy his chances against Cilic, despite losing his only match to him in two sets in Shanghai last year.
"Really I can go out there and do my best. I'm in a good place," he said.
Cilic is bullish about his form heading into the business end of the tournament, having got past 10th seed Pablo Carreno Busta and Nadal to play off for a spot in Sunday's final.
"I'm extremely pleased with my own game. Even in the other matches before the Nadal one, I played great tennis. Very high level," Cilic said.
"I want to keep going with my own game and try to lift up, keep pushing as much as I can."
Cilic, who lost to Roger Federer in last year's Wimbledon final, has been serving impressively with a total of 96 aces and a fastest serve clocked at 180 mph.
He has won 81 percent of his first serve points and 54 percent of his second serve points, while breaking his opponents' serve 23 times.
Cilic sees facing the unseeded Edmund as a great opportunity to make his third Grand Slam final and first in Melbourne.
"Kyle has had an amazing run, winning a lot of tough matches and playing great tennis," Cilic said.
"He's also very entertaining to watch. Big hitter, great serve, great forehand. Plays great on the hard courts.
"For me, obviously on the paper it's probably easier to play him than Rafa. But still he deserves a lot to be here."
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