The 23-year-old midfielder, who has returned to Charlotte FC in the United States after a loan spell with English Championship outfit Birmingham City, is said to have caught Celtic manager Ange Postecoglou’s eye.
McGree has been one of Birmingham’s best players this season, but with his loan deal having expired, Celtic are now free to make their move for the seven-times capped midfielder, who is said to be valued at £2million.
The Mail on Sunday reports that Celtic are about to fend off competition from several other Championship clubs to land McGree and that a deal could be done next week.
McGree started his career at Adelaide United in his homeland and has had spells with Club Brugge in Belgium as well as loan stints with Newcastle Jets and Melbourne City.
He made his debut for Australia last year and has earned seven caps during the Socceroos’ World Cup qualifying campaign.
The news that Celtic are closing in on McGree will come as a blow to Birmingham manager Lee Bowyer, who was hopeful of keeping him at St Andrews for the second half of the season.
McGree originally joined for the 2020/21 campaign, but the Blues were able to extend his loan by another six months into this season.
Middlesbrough have also been linked with a move for McGree and were expected to be the favourites to land his signature, but now Celtic have moved in.
McGree plays in central midfield and has scored three goals in 30 appearances for Birmingham this season.