Brailsford told Sky Sports that a historic treble bid "looks attractive".
"Winning the big races intermittently is great, but ultimately, the challenge is to maintain that level of performance over a long period of time," he said.
"At a preliminary stage, I don't see why we can't go for all three Grand Tours and have a real good crack at that. It's very premature, but that would certainly be something that looks attractive next year.
Brailsford also signalled that a major one-day victory - something that has eluded the British team thus far - is on the cards.
"We still want a Monument. We have got to put a lot of thought and effort into that next year, for sure," he said.
Sky has recently signed a number of riders that will support these ambitions, especially Astana's Mikel Landa and Etixx QuickStep's Michal Kwiatkowski. Landa is expected to take the place of departing Richie Porte in Sky's Grand Tour line up - potentially even as a race leader - while Kwiatkowski will bolster Sky's Ardennes Classics team.
Other new recruits include Michal Golas, Benat Intxausti, Gianni Moscon, and Danny van Poppel.
Race planning isn't the only preparation for 2016 going on at Sky HQ, either, with new kit rolling off the production line as well. Fans hoping for a departure from the black-and-blue may be disappointed, however.
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