The former Brisbane Roar captain has signed with the reigning SPL champions but is still waiting for his visa which should come through later this week.
But even if the paperwork is complete, ‘Gers boss Ally McCoist will not play the 28-year old midfielder as he has Australian national team duties against Thailand in Brisbane on September 2.
McCoist did reveal that McKay’s fellow new signing, Alejandro Bedoya, should be right for Sunday’s visit of the Dons to Ibrox.
“It’s great that Alejandro will be with us this week but Matt will be different,” McCoist told the club’s official website.
“He might get his visa before the end of the week but we have to take into account that he has international responsibilities the following week.
“I’m not sure it would be a good idea for him to fly across the world then back again in the space of three or four days.
“So that’s something we will need to think about but we look forward to welcoming Alejandro in to our group.”