Ryan was due to be at Murray Park this week for a 10-day spell but suffered the injury while playing for Central Coast Mariners against Western Sydney Wanderers in the A-League on Sunday.
According to his club, the trial had been "indefinitely postponed", however Ryan is set to face Melbourne Victory this Saturday before making the trip to Scotland.
Ryan comes highly recommended by former Rangers midfielder Ian Ferguson, who is in charge at Perth Glory, and a successful trial could lead to a move once their transfer embargo is lifted later this year.
McCoist said: "We've been informed Mat has had to go for a scan after a small injury last weekend and we're hopeful things have just been put back a week.
"I've been told by his representatives he'll be due to arrive in Scotland on Sunday night or Monday.
"We've watched videos of him and I've spoken to Fergie over at Perth Glory about him along with one or two of the boys in Australia. He's had nothing but glowing reports. He's a young goalkeeper with huge potential and I look forward to seeing him."