A club source confirmed the Sky Blues were in discussions with McGowan’s agent over the 29-year-old filling the void left by Aaron Calver, who has signed for expansion club Western United.
Much-travelled McGowan was released by Bradford City at the end of this season, having spent the back end of the campaign on loan at Dundee.
It was a bad year for all parties though - with the Bantams relegated to England's League Two and Dundee dropping to the Scottish Championship.
McGowan did, at least, see plenty of action, making 15 Scottish Premiership appearances and 23 in League One.
The 20-cap McGowan - who featured for Australia at the 2014 FIFA World Cup - has never tasted the A-League with previous stints at Hearts, Shandong Luneng, Dundee United, Henan Jianye and Al Sharjah amongst others.
It’s understood the Sky Blues are offering a multi-year deal, and are favourites to get their man ahead of other interested parties, including Melbourne Victory, Melbourne City, Adelaide United and Wellington Phoenix.