EPCR, the tournament's organisers, have confirmed four possible venues for this season's semi-finals.
Franco Smith's side must first overcome three-time champions Toulon at Scotstoun this Saturday. Victory would set up a semi-final clash against either Leinster or Sale Sharks, with a place in the final at stake. This year's final is scheduled for May 23 at San Mames Stadium in Bilbao.
Glasgow secured a home path through the knockout rounds after topping their pool with a maximum 20 points, thanks to bonus-point wins over Sale Sharks, Toulouse, Clermont Auvergne, and Saracens. They finished as the second overall seed, behind defending champions Bordeaux Begles, who edged them on points difference.
Although the semi-final would not be played at Scotstoun, Glasgow would still benefit from home-country advantage at Murrayfield.
Possible Champions Cup semi-final matches and venues
Union Bordeaux Begles (1) v Bath Rugby (4) or Northampton Saints (5)
Stade Atlantique Bordeaux Metropole, Bordeaux (capacity: 42,100)
Glasgow Warriors (2) v Leinster Rugby (3) or Sale Sharks (11)
Scottish Gas Murrayfield Stadium, Edinburgh (capacity: 67,130)
Leinster Rugby (3) v RC Toulon (7)
Aviva Stadium, Dublin (capacity: 51,700)
Bath Rugby (4) v Stade Toulousain (8)
Stadium MK, Milton Keynes (capacity: 30,500)
Northampton Saints (5) v Stade Toulousain (8)
Stadium MK, Milton Keynes (capacity: 30,500)
RC Toulon (7) v Sale Sharks (11)
Stade Atlantique Bordeaux Metropole, Bordeaux (capacity: 42,100)