Edmund defeated France’s Tristan Lamasine 6-4 6-2 in the first round of qualifying in Melbourne on Wednesday and then saw off the challenge of Austin Krajicek of the United States in three sets.
He now faces Dane Propoggia of Australia in the final qualifying round on Friday.
The 20-year-old, who has split with coach Greg Rusedski due to the former US Open finalist’s broadcast and family commitments, is now one win away from qualifying for the Australian Open.
Edmund has risen to No 192 in the world, the third highest Briton, after winning two titles on the Futures Tour in 2014.
“My aim at the start of last year was to finish with a ‘one’ next to my name,” said Edmund.
“And I did it in the last tournament. I think it is a nice platform: I ended the year on a high.”
His ambition for 2015 is to evolve his style of play, which in turn should see him continue his climb up the rankings.
“I have an aggressive game style - I like to use my serve and my forehand as a weapon,” he said.
“I’d like to come forward a bit more: sometimes I use my forehand well, but then don’t take advantage of that as well as I could.
“It’s obviously easier said than done. In certain situations, you’re a bit hesitant to come forward because these days the guys move so well, and if they get a racquet on the ball they have half a chance of passing you.”
Edmund, who is now working full-time with the LTA’s head coach James Trotman, spent time last month at Andy Murray’s training camp in Florida.
He remains in touch with Rusedski, who he confesses gave him the confidence in the past to make tough decisions over coaches.
Edmund said: “One of the first things Greg said to me was: ‘You’ve got to be selfish, and you’ve got to do what’s right for you,’.
“Making a decision with Greg was a tough decision – when you’re making a change in your set-up, it’s not something you just think about in two minutes, it’s a process you go through.
“You weigh up options and have to get the best for yourself.”