How do they expect to balance this? Even if the engines were mounted at the very end, it will likely be very nose heavy with the wings so far aft. It may need Canards and/or F18 type Leading Edge Root Extensions(LERX).

I don't know technical issues much, but I would sure buy one if I had like 100 mil lying around. But I would pay more if it looker like SR 71. Given all other aspects remain constant. This does not look cool enough for 2013/2014.

Is there some reason the Concorde is not counted as a supersonic business jet?

Thought the same thing - stall speed very high unless some non-visible mechanism creates balance/lift at the front of the aircraft.

Or you could buy a Gulfstream G650 for the same price and cruise at M 0.9+, have twice the range and fly in comfort and luxury with greater cross-sectional area and head room. One of the problems with the Concorde was that for the same price you could either fly fast and be cramped (it was an incredibly small cabin and felt like coach) or take the time and fly in first class. Which will matter more to those that can afford such a vehicle: speed or luxury?

The Concorde carried 100 passengers and flew with load rates of 70%+. A tragic accident in 2000 and then 9/11 led to the Concorde's cancellation in 2003. But demand for supersonic travel and willingness to pay for premium tickets was well established. It is about time for a next generation Concorde.
The Concorde was designed in the 1960s with slide rules and built just a few years after AT&Ts Princess telephone. Since then, there have been a lot of new technologies in composites, engines and avionics. These can be used to increase fuel efficiency, reduce noise and improve safety.
David: In this aircraft, the center of gravity is a function of the positioning of the fuel tanks. It is controlled during flight by regulating fuel consumption from each tank.
Victor: In this case, business jets are considered aircraft with less than 20 passengers or under a certain max weight. The Concorde with 100 passengers was considered an airliner.
JDJacob: good question. Is time more important than luxury?

@ Mirmillion
Balance issues do not notably affect stall speed.
@ JDJacob
For hours in coach or eight in first class? No contest; coach.

With time and luxury, it's not an either/or situation. Small business aircraft, that are extremely cramped, sell well because the flight times are short, so it seems the degree of comfort desired is a function of flight time.
Operating cost is another factor that seems to be missing, and supersonic aircraft will be much more expensive to operate. It would be interesting to have an extended exchange with business leaders comparing the comfort and economy possible with a blended wing/body subsonic aircraft to the shorter flight time of a narrow-bodied, fuel-hungry supersonic.

The wing does not look at all like a supersonic wing. Supersonic wings are typically swept back quite a bit. Even aircraft that fly close to the speed of sound have swept wings. This wing has a somewhat straight planform that would be good for low speed flight.
The landing gear seems unnecessarily tall. Gear that tall wouldn't be able to fold back into a the wing as shown. Look at the head-on rendering. The wing is impossibly thin. The strut of the landing gear is thicker than the wing itself. The rear landing gear looks like it folds inward so that the wheels end up inside the fuselage. However, the wheels are cartoonishly large. No way they would fit. The landing gear doors in the front are ridiculously small. Their small size suggest that the front gear telescopes straight down, from underneath the cockpit area. Again, there is no way they could fit there.
As far as the center of gravity is concerned, I actually do think the plane could balance in the configuration shown. Remember that even a full cabin is still mostly empty space. The engines are big chunks of metal that are much more dense than the rest of the aircraft.
All things considered, I think this is a badly done "artist's concept" of a futuristic plane from the 1960s.

Hey Ben - I really hope that you are joking. I can assure you that those wings are superbly designed as an aerodynamic compromise between fuel efficient (relatively speaking) supersonic flight and high transonic flight speeds. If you think that all supersonic wings are heavily swept, I refer you to the F104. As for the undercarriage, although this is obviously an artist's impression, the angle of attack at take-off and landing in an aircraft of this nature will likely be extremely high, hence the need for a rather elongated landing gear.