Toulon, who beat ASM Clermont Auvergne to win the title in Dublin in May, have never been beaten at home in the Heineken Cup and will be looking to add Glasgow's scalp to the seven that have gone before.
In fact, you have to go back to the last round of the Pool matches in the Amlin Challenge Cup in 2008/09 for the last time Toulon were beaten at home in Europe, 37-19 by Bristol. Since then they have won 16 successive European matches on their own patch.
It all adds up to a highly pressurised weekend for Al Kellock's men, who have only one win and a draw on 13 previous Heineken Cup trips to France.
"Pressure to me is what comes from the opposition, their line-speed and how quickly they get on ball, not the outside influences. I don't know what it will mean to the French media or Toulon players us being on top of the PRO12," Glasgow head coach Gregor Townsend told The Scotsman.
"I'm sure they will prepare well for us and it's just a great occasion to be involved in. We have a focus on what we need to do at the weekend and knowing that we have to perform to beat these teams.
"We are going to have to play close to our best to have any chance of winning this game. I watched Toulon beat Clermont before our game last weekend, and they are two of the best sides in Europe. But we can't wait."
A fine 17-12 win at the Scarlets carried Glasgow back to the top of the PRO12 table last weekend and put them in the right mood to head to the south of France to face a team that is joint top of the Top 14 with Toulouse.
Townsend has used 36 players to date this season, but knows he will have to choose his top team for Sunday against a side that might just give Heineken Cup debts to the likes of Bryan Habana, Juan Smith, Drew Mitchell and Ali Williams
"We're playing well enough right now to win games. The Leinster game produced some of the best performances I've seen from our forwards especially. But I've watched a lot of rugby from around the world, and a lot of teams are rusty at this point," added Townsend.
"I've watched a lot of French rugby and it isn't very fluent yet. We've got six months of a season still to play and at the moment defences are on top and we're all trying to work out the scrums.
"We couldn't have asked for more than five wins from five to go into Europe. We've spent a lot of time looking at both of our first European opponents, Toulon and Exeter, and we'll have a game-plan that we believe could lead to success."