Speaking to Warriors TV, forwards coach Jonathan Humphreys revealed that there was a certain sense of inevitability about the draw amongst the former Scotland coaching staff.
He said: "We talked to Vern (Cotter) about this a fair bit during the 6 Nations - we were convinced it was going to happen!
"We've worked together for a long time, so we know what the strengths and the style of play of Montpellier will be, although we said we would double-bluff each other. It's a really exciting group and we're looking forward to it."
The former Wales international is looking forward to his first taste of the European Champions Cup as a Warriors coach, and is confident that free-flowing rugby will grace the Scotstoun pitch in the new campaign.
"International rugby is a fantastic experience, but it's great to be back in club rugby and with the chance to do something special," said Humphreys.
"There's a slightly different atmosphere on European nights than in the Guinness PRO12.
"Leinster, like a lot of the Irish teams, seem to base their season around the European campaign, so we'd expect them to have their best players available and really go for it.
"Leinster, Exeter and Montpellier all want to play a good brand of rugby, so I think it's going to be a really good tournament for the spectators."
Assistant coach Kenny Murray is also relishing the challenges posed by Glasgow's European opponents.
He said: "We've had a lot of chat over the last few days as to who we might get, and I think Jason (O'Halloran) and Jon (Humphreys), having worked with Vern, were quite keen to get Montpellier.
"It's a really challenging and exciting group. We've played Exeter before and enjoyed that experience, and they'll be on a high after winning the Premiership.
"The atmosphere here when we play the Irish sides is always outstanding, so I expect it'll be the same again when Leinster come here. We're looking forward to those nights because it's great for our club and our city."
Glasgow centurion Chris Fusaro is anticipating the group to be close, but is confident that the Warrior Nation can play their part in another historic European campaign.
He explained: "The general intensity of the Champions Cup means the games always have a different edge. Exeter play a great brand of rugby and are a team we've enjoyed playing in the past, and Montpellier are one of the French giants. It's always tough against them, and I'm sure Vern going there will bring an attacking edge to their game - there are no easy pools.
"It'll probably be like a massive game of chess, with all the coaches knowing each other. It'll be tough, but when our crowd gets behind us, Scotstoun is a great place to play."