Owen, 33, who scored 40 goals in 89 internationals for England and had stints at Liverpool, Real Madrid and Manchester United, is currently playing for Stoke City in the English Premier League.
Glory have one spare position in their squad for an international player after releasing Irish striker Billy Mehmet this week and do not have a marquee player.
The West Australian newspaper said if Owen was recruited as the club's marquee player, his wages would not be included in the competition's salary cap.
A Glory spokesman confirmed the club was interested in securing Owen's services, but said negotiations were in their infancy.
"Michael Owen's agent has enquired about Michael playing in the A-League," the spokesman told the newspaper.
"Perth Glory are interested but are yet to find out Michael's terms and conditions.
"Until these are known, Perth Glory will not enter any further negotiations."
If Owen joins Glory he will become the fourth high-profile international player in this season's A-League, along with Italy's Alessandro Del Piero, Japan's Shinji Ono and England striker Emile Heskey.