The 18-year-old is on the Hoops’ radar, according to former Dundee star Albert Kidd, who is now technical director at the A-League champions' rivals Adelaide Olympic.
Kidd claims Celtic scout Tosh McKinlay has been monitoring the youngster, who has been called up for his nation’s upcoming World Cup qualifiers against Iraq and United Arab Emirates.
He said: "I'm in very close contact with my ex-team-mate Tosh McKinlay and we have talked about Riley McGree. They are showing a lot of interest."
McGree came through the ranks at his local youth side Gawler Eagles and also spent time at the Football Federation South Australian National Training Centre before being snapped up by Adelaide United in 2014.