This question gets asked far too much. There's a couple of limitations that will prevent this from ever realistically happening.
First, simply put, the 3DS's internal NAND doesn't hold much, at most you'd be able to have a small handful of smaller DS games on there. As for the larger games, maybe ~3? It'd be a pain having to swap those out.
Second, DSi is a bit more than just a souped up DS. The DS games would have to be ported to DSiWare, which is pretty much impossible without the sourcecode. Technically, some very talented coder, with poor priorities and too much free time, might be able to create a wrapper that translates, adapts, and points to new hardware. It might still be impossible, though as I'm not entirely sure of DSiWare's limitations.
Even if it is possible, I wouldn't consider that realistic, though, as why would someone go through that much work when people can just grab a $20 flashcart? Especially since it'd be more convenient, since it wouldn't suffer the space restrictions of the 3DS's NAND.