Wolves' Bakary Sako has revealed he is mulling over offers from the Premier League but is yet to decide on his future.
Rotherham boss Steve Evans will decide the fate of his out-of-contract players in a meeting on Monday.
The Australian was prevented from travelling to Scotland for a 10-day spell this week due to a shoulder problem.
The 20-year-old Central Coast Mariners keeper sustained the injury while playing 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 the UK.
Capped twice at full international level, Ryan comes highly recommended by former Light Blues midfielder Ian Ferguson.
A transfer embargo means Rangers are unable to recruit new players this month but a successful trial could earn the youngster a switch to Ibrox after the ban is lifted.
Boss Ally McCoist told the club's 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."