Glory is reportedly in talks with the former Liverpool and Manchester United forward's management about signing him as the club's marquee player to replace Billy Mehmet.
Glory coach Ian Ferguson has already sounded out possible replacements and is keen to secure a player in January transfer window.
A Glory spokesman confirmed the club was interested in securing Owen's services but said negotiations were in their early stages.
"Michael Owen's agent has enquired about Michael playing in the A-League," the spokesman told the West Australian 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."
Owen, who scored 40 goals in 89 internationals for England and had stints at Liverpool, Real Madrid and Manchester United, is currently with Stoke City in the English Premier League.
The 33-year-old, who is one of England's most successful strikers in recent years, having scored 118 goals in 216 league appearances for Liverpool, is not getting regular game time at Stoke and is believed to be keen to make a move.
However, he is set for a rare appearance this weekend when Stoke plays Crystal Palace in the FA Cup third round on Saturday.
Glory has a spot available for an international player after announcing the transfer of Mehmet to Thailand outfit Bangkok Glass FC on Friday.
"We have got one or two irons in the fire overseas and we're waiting to see what happens with those, whether they are still progressing," Ferguson said on Friday.
"We have put a couple of things to certain players and hopefully if it comes off, it'll be great for Perth Glory."
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 his former England strike partner Emile Heskey.
Fifth-place Perth plays host to rock-bottom Sydney FC on Saturday night with the club announcing the nib Stadium fixture is a sell-out, with Alessandro Del Piero's arrival in the west creating unprecedented demand for tickets.