Remember, this is shaky. The best The Sun can do is cite an anonymous source -- and all this alleged source says is that Boyle has been offered the film, not that he's accepted, or is even seriously considering it. It seems reasonable that the offer would be made, though. Obviously he's in high demand after winning the Oscar last week, and at various times all sorts of directors, from Tarantino to Spielberg, have been rumored to be interested in making a Bond film. Furthermore, Boyle is British, which used to be a prerequisite for a Bond director but has not been enforced lately.
The question is, would he be a good fit? One of the things I like about Boyle is that he's proven adept at an astonishing variety of genres, from horror to whimsy to sci-fi to whatever Slumdog was. I have no doubt he could make a full-bore espionage caper if he wanted to, and he could probably dig the franchise out of the Jason Bourne-copying rut it got stuck in with Quantum of Solace.
On the other hand, maybe a director as visionary and talented as Boyle ought to do anything BUT the 23rd entry in a 47-year-old franchise. The Broccoli family, which owns the Bond character and produces the films, is famously skittish about messing with the formula. They generally want a director who will do what they tell him, not get all inventive and visionary on them.
Bearing in mind that it may never happen anyway, join us in a little speculation, won't you? What would a Boyle-directed 007 film be like? Would it be a good or bad move for him and for the franchise? Feel free to speculate on possible titles, too, such as Die Another 28 Days Later.