Assistant ciach Nigel Carolan has stressed the importance of focusing on performance rather than the occasion.
"I think we don't want to let the opportunity go or the occasion, but we don't want to play the occasion," Carolan told The Scotsman. "We want to be able to just play the game that's in front of us. I think it's important that we respect the opposition rather than assuming that just because we've got a home quarter-final that that's going to be enough to get us across the line.
"Based on our own foundations of a team, we're built upon hard work. We're built upon effort. We're built upon detail. If we don't bring that, just by being at home is not going to be enough for us."
Glasgow earned home advantage through a strong pool-stage campaign and now sit one win away from a historic semi-final.
"It's huge for the club," added Carolan. "We've put ourselves into this position by how we've performed in the pool stage and a very gritty game against Bulls at the weekend in horrible conditions.
"We're within touching distance of a semi-final and to have that in Murrayfield would be huge, but we can't look that far ahead. We can only look at what happens this weekend first."
Despite Toulon's poor domestic form, Carolan insists they remain a serious threat.
"I think that's the nature of the Top 14," he said. "You see the same with La Rochelle. They're at the top of the table one year and they're struggling this year. It's a very competitive league, but when you look at the makeup of the [Toulon] squad, it's littered with real quality players, both French and foreign. Just where they're sitting in the Top 14 table, we don't really look at that at the moment.
"They're still a huge team. They have a history in this competition, they've won it numerous times, so they know what it takes to win this too."