Federer saw off Stan Wawrinka in less than an hour on Tuesday night, winning 6-3, 6-4 against his Swiss compatriot.
That sets Federer up with a first career showdown with Edmund, who is in good rhythm at the moment.
The British No 1 eased past Radu Albot in the third round as he continues what has been a strong spell in the Californian desert.
Edmund won a Challenger event in Indian Wells last week to aid his comeback from a knee injury.
Federer and the 24-year-old have practiced together on numerous occasions and were both part of Team Europe for the 2018 Laver Cup last September.
And 20-time Grand Slam champion Federer is wary that Edmund has played regularly over the past fortnight and will be relishing his first match against him.
Speaking after his win over Wawrinka, Federer said of his upcoming meeting with Edmund: “It’s tricky. Especially because he’s established already.
“I think he’s a really good player, Kyle, great forehand, unbelievable power there. Great mover, good balance.
“He’s just won the Challenger here this week in Indian Wells so he’s played a bunch of matches – more than anybody else really in this event. I think it’s a good advantage for him.
“He also came through very convincing in the last couple of matches. I think he’s ready to go.
“We had a great week with him in Chicago at the Laver Cup. I could see what he had as a person and as a player and I was highly impressed.”
Federer, however, insists he is in strong shape as he looks for back-to-back titles after clinching the 100th triumph of his career in Dubai earlier this month.
He added: “I think I’m feeling good. It’s a big difference to the beginning of the tournament in Dubai.
“Of course it was also more windy and I hadn’t played in a while. I think I’m back in the point-for-point mentality.
“I’m not overly panicky when big moments come about in the match. I’ve got clarity and that always comes when you’re playing enough tennis.
“Plus I’ve no pain in the body, I’m very happy where I am right now.”