It is not just that he and his Saracens team-mates are heading for the febrile arena that is the Stade Ernest Wallon in Toulouse, but that they go into the Heineken Cup weekend's marquee game as decent favourites to win.
That status has been earned by the north London side's run of 10 consecutive victories across all competitions, although the recent woes of their opponents - Toulouse are in an uncharacteristically lowly fourth place in France's Top 14 championship - has also fuelled speculation that a famous victory could be on the cards. Having lifted the trophy four times, Toulouse may be the most successful side in Heineken Cup history, but their crown has slipped recently, and most dramatically of all when they went down 16-14 at home to Connacht just over a month ago.
The result was greeted with gasps by most followers of the European rugby scene, but it brought a wry smile of recollection to the face of Brown. When he saw what Connacht had done, his mind sped back to that January day in 2009 when he and his Glasgow confreres had also toppled Toulouse on their home patch, grabbing a 33-26 win that was immediately billed as the greatest upset the tournament had seen.
"This will be my first time back," said the 31-year-old forward, who clearly relishes the prospect of his return visit. "It was a very special day with Glasgow. We went over there and no one was expecting anything from us. It wasn't just that we won, it was also the manner of it as we scored three or four tries and just played some really attractive, open rugby.
"I actually scored in that game, and I've not scored many since. But the Evans brothers were absolutely on fire for us that day. Max got a try and Thom was looking lethal as well. It was probably the best result we had in all my time at Glasgow."
Well, up to a point. The fact of the matter was that Glasgow's European ambitions had already been extinguished that season, and there was nothing more than pride at stake. The scenario today is rather different as Saracens and Toulouse sit joint top of Pool 3, with 15 points apiece, and the side who win this afternoon will almost certainly book their passage into the knockout stages.
The wind is unquestionably at Saracens' back, but Toulouse have the European pedigree. Against the French side's quartet of victories, all Saracens have to offer is two appearances in the semi-finals.
For much of their recent history, Saracens have been dismissed as too one-dimensional, too reliant on a powerful, but lumbering, forward-oriented game. The theory was that what worked in the attritional environs of the Aviva Premiership (they won their first - and only - domestic championship title three seasons ago) was found wanting on the European stage. There might still be some truth in that, but Brown believes his team have evolved a more rounded game.
"It is going well," he said. "We have lost a couple of games, but we have been winning a lot more. Really, though, it is the manner in which we have been winning that has been really satisfying.
"We have been scoring quite a lot of tries, but at the same time we have kept our defence tight. The main thing is that we have built on the cornerstones of the last few seasons - our set-piece, our defence and our kicking game - but our attack has been pretty lethal this year as well."
The portrayal of Saracens as carthorses was always a caricature too far. Yes, they had some serious piano-shifters up front, but they also had some virtuoso ivory-tinklers in the backline in players like Chris Ashton, Brad Barritt and David Strettle. According to Brown, the whole thing is now coming together as one.
"It is just about us as a side learning and growing," he said. "I do feel that we are a more rounded side now, but we have to keep improving and looking forward."
But still, he will allow himself a glance in the rear-view mirror as he prepares to step back out on the pitch where he and Glasgow enjoyed their finest European hours. "The feeling in the squad that day was great," he recalls. "But then it always has been. We were over in France and we had nothing to lose. We just thought 'let's go out there and play as we can'. We knew that if we did that we could put them under pressure. That's what we did and ultimately that's how we got the win."
A recipe for today? Perhaps not. "Toulouse have had some bad results away, but they have won most of their games at home, which is typical of a lot of French teams. We're confident, but they will be right up for this one.
"No disrespect to Connacht, but I imagine Toulouse will be a bit more wary about the threat we can pose. There is no way they will underestimate us or expect an easy game. They are a side packed with absolute monsters. We're going over there expecting a war."
Toulouse v Saracens is live on Sky Sports 2, today, from 2.45pm