Ryan injured a shoulder playing for Central Coast Mariners in their 2-0 win over Western Sydney Wanderers at the weekend.
The knock is described as "minor" by his A-League club and he is expected to be back in action in time for the meeting with Melbourne Victory on Saturday.
A statement on the Rangers website stated: "Both clubs have agreed that it is in Ryan's best interests to remain in Australia under the care of the Mariners' medical department for the foreseeable future."
Meanwhile, former Aston Villa, Manchester United and Australia keeper Mark Bosnich reckons Ryan, who Rangers could register on September 1 after their transfer ban ends, should snub the move
He said: It's ridiculous. This is one of Australia's best young talents and he's going to the fourth tier of Scottish football.
"The Scottish Premier League isn't as good as the A-League."