Hate to rain on anyone's parade, but this rumor is totally untrue.
Here's the skinny: BMW had floated reviving one of its old British marque names, then let it die...then revisited it to help bolster sales in Mini dealerships, which are having trouble making ends meet. (Mini dealerships must be independent of BMW dealerships!)
But the Triumph name has NEVER been seriously considered.
If any car is to be revived, it would most likely be the Austin Healey nameplate, because it carries more name recognition and better brand identity (simply because the marque died before the horrible problems of the 1970s.)
In addition, the Healey was always positioned above Triumph and below Jaguar, which translates well to being below a Z4, but above Miata, Pontiac Soltice, Pontiac Sky.
The original plan was for a return of the Bug Eyed Sprite, and there were even design sketches. The Sprite would fit very well with the Mini brand. It is also possible to get a Healey 3000, since BMW uses a 3.0L inline six, but I haven't heard of anything from any sources that indicates they have chosen this route. (Just my personal speculation.)
BUT don't hold your breath, as any possible return won't happen before 2010.