But the Hoops skipper remains very much grounded when he hears fans chant about 10-in-a-row - with one Scottish bookie pricing that up at a miserly 6/4.
"That's a long, long way off," is his response.
Given what has happened in the Scottish game over the period it has taken Celtic to make it a hat-trick of titles, that's understandable.
Anyone who believes they can predict with any degree of certainty who is going to be doing what - and where - seven years from now is either naive or totally detached from reality. Which is why Brown's horizon extends no further than next season.
There is enough to be done in that period to keep him fully occupied, starting with qualifying for the group stage of the Champions League for the third year on the trot, and successfully defending the championship, which is Celtic's passport to competing in Europe.
Brown is confident the Hoops squad which embarks on these challenges will be in a better condition to do so than they were at the start of this campaign.
His reasoning is that the intake of new Bhoys, who were sampling it all for the first time this term, will know what is about to hit them.
Of course, Neil Lennon's careful rebuilding following the departure of core players from his team - Victor Wanyama, Gary Hooper, Kelvin Wilson and Joe Ledley - could be undermined if there are more big-name sales this summer.
Fraser Forster and Virgil van Dijk are expected to be the subject of big bids which the club could struggle to resist, while Georgios Samaras - the second-longest serving player at the club behind Brown - is running down his contract.
But the skipper believes the Bhoys who have just discovered what it feels like to win a trophy with Celtic - including Stefan Johansen, Nir Biton and Leigh Griffiths - will be even better for the experience.
And, augmented by whoever Lennon succeeds in bringing in when the window reopens, the squad will be ready to get into gear once again when the tapes got up for the qualifiers in mid-July.
Brown said: "I definitely think the boys who are new to the club are starting to realise what is involved in winning trophies here.
"There have been a lot of new faces in the past year, and it has been hard for them to get used to playing for this club."
Brown has to go back to the summer of 2007 to remember what it felt like to be a new Bhoy arriving at Parkhead.
Back then, he was Gordon Strachan's most expensive signing at £4.4million from Hibs - an outlay which has not been surpassed by Celtic since.
He had the advantage of having played against the Hoops for a number of seasons prior to joining the club, so had a very good idea of exactly what he was walking into, and the expectation which surrounds playing for Celtic.
Griffiths has followed a similar path from Easter Road, albeit via his parent club, Wolves, for half a season.
And Brown has been very impressed by the way his travelling companion from Edinburgh has made the transition.
"He has been flying since he came here," said Brown of the 23-year-old striker, who has hit five goals in his first nine appearances.
"More importantly, Leigh has not just made an instant impact, he has managed to keep it going, as well."
Other recruits have had to light a longer fuse before their career in green and white has ignited.
Nir Biton is a case in point, the Israeli midfielder struggling with the pace and physicality after arriving last summer, before finally getting into his stride since the turn of the year.
Only injury sustained while on international duty last month has halted his development, but Biton is due back within the next fortnight to continue his steep learning curve as a Celt.
As dressing room leader, Brown has been something of a mentor for Biton, reassuring him he will settle into his new team, club and environment.
The skipper understands how daunting it all can be, exacerbated by the need to be winning every game.
"This is such a huge club, and I don't think foreign players coming here understand just how big Celtic is, not just in Scotland, but in the rest of the world," said Brown.
"It's just incredible. On Saturday, we had nearly 50,000 turn up just to see us play against Ross County in the game after we became champions again."
Johansen is another who has hit the ground running. And the 23-year-old Norwegian never tires of reiterating that, if you can't handle the pressure of playing in front of big crowds with such expectation, you are at the wrong club.
Brown likes that approach, underlining, as it does, that the young midfielder is aware of his surroundings and responsibilities.
"You come here to win games, to win trophies and because you want to be a champion," said the captain, who will lift the Premiership prize in Celtic's final home game. "Stefan has done all of that. He has played really well since arriving in January.
"Getting players like him and Leigh in during the season, rather than at the start of next, is a bonus for the club."
Brown is very much the constant in an ever-changing Celtic tableaux, and he anticipates the picture will continue to alter.
It is another aspect of playing for a club this size and with this ambition which he reckons everyone who signs up to wear the Hoops has to not only accept, but embrace.
The evolution has no start and no end, and Brown said: "There are always players coming in and players going out.
"Other clubs want to buy our top players, and it is always hard for us to try and keep them here, especially when they want to go to England to play in the Premier League.
"But we have still got to try to keep our best players, if we can."