Glory are under investigation by Football Federation Australia for salary cap irregularities, while the Western Australian club have not won in four A-League matches.
To add to their misery, two Glory players - striker Andy Keogh and defender Josh Risdon - were arrested for disorderly conduct after last weekend's 1-1 draw away to Adelaide United.
Perth have fined the duo, although they will be available for Glory's trip to Victoria to take on City on Sunday.
Kenny Lowe's Perth have not won since the A-League resumed after the Asian Cup but remain on top of the A-League by a point from second-placed Melbourne Victory.
City will welcome Glory to AAMI Park having not scored in two matches, but will be banking on their home record to return to the winners' list.
John van 't Schip's men drew 0-0 away to Wellington Phoenix last week and were thumped 3-0 by archrivals Victory a fortnight ago, but City have scored in 17 straight matches at their home ground - including three wins in their past four.
When Glory visited City in Melbourne on Boxing Day, Perth came from behind to draw 1-1.
If Lowe's side fail to win, it could see Victory end the round on top of the standings.
Victory travel to Brisbane Roar on Friday, looking to stretch their unbeaten run to five matches, and they should be confident as they have scored 11 goals in their past four fixtures, although two have ended in 3-3 draws.
If Victory win in Brisbane they will move to 36 points, while Perth sit on 34 heading into round 18.
On Saturday, Central Coast Mariners will travel south to take on Sydney FC and Adelaide United will host Western Sydney Wanderers.
The Mariners were dumped out of the AFC Champions League by China's Guangzhou R&F in a qualifier on Tuesday and will be keen to bounce back against Sydney.
On Sunday, Wellington Phoenix will take on Newcastle Jets.
