The 20-year-old is highly rated in his homeland and has caught the attention of Light Blues manager Ally McCoist.
Pundits Down Under have criticised the move, but Ryan is keen to train in Glasgow and if his time here is successful, he could be someone the club looks to recruit when it is able to register players again later this year.
The youngster is currently contracted to Central Coast Mariners but hurt himself playing against Western Sydney Wanderers in the A-League on Sunday.
He could face Melbourne Victory in Launceston this Saturday and is then scheduled to make the trip to the UK.
And McCoist has revealed he comes highly recommended by a number of his contacts in that part of the world, including Nine-in-a-Row legend Ian Ferguson.
The manager said on the club website: "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."