The 24-year-old shot a second-round 67 to move to three-under-par at the halfway stage in Aviemore.
He's five behind the leader, fellow Scot George Murray, and was delighted to end a miserable run of five consecutive cuts on the Challenge Tour.
The Archerfield Links player said: "I finished badly here last year (with a second-round 77] to just miss the cut so I've made up for that."
McIlroy is still riding on the crest of a wave after his sensational win on the PGA Tour earlier in the season, while Davies is the man of the moment of Europe after back-to-back runner-up finishes.
Davies was also playing on the Challenge Tour this time last year and Saltman is confident he can join the Welshman on the main circuit before too long.
"It wasn't that long ago that Rhys didn't have a European Tour category but now he's won nearly 1 million," said the Scot. "He stayed patient and I'll do the same because I know I have the ability and attitude."
Also on three-under at the start of today's third round in Aviemore was defending champion Jamie McLeary, who lives near Bonnyrigg.
He picked up four birdies in his last six holes for a 68.
Lloyd's older brother, Elliot, was the only other Lothians player to survive the cut, making it on the mark after a 73 put him on level-par for the tournament.