However, because Rangers are under a transfer embargo following financial problems at the Ibrox club, Ryan is bidding to earn a move to Glasgow in September when the embargo is due to end.
Ryan is due in Glasgow on Monday to spend 10 days training with the Irn-Bru Third Division club.
The 20-year-old, who has played for Australia in East Asian Cup qualifying games, is set to link up with Rangers after Mariners football manager Lawrie McKinna arranged the move with Rangers boss Ally McCoist.
"I was in Scotland over Christmas and spoke with Ally McCoist about Mathew Ryan," said McKinna.
"It is a credit to Mat and to our club that Ally was well aware of Mat's ability and potential and immediately offered for him to join Rangers for a training spell.
"Mat is eager to take up the opportunity and we are sure he will learn a lot from the experience."
Ryan has three months remaining on his current contract with Central Coast.