I like the Broadcom rumor as it makes sense but the AMD option is very interesting as well. The OMAP family might play well with / compliment the current AMD fusion family and together AMD might be is a better position to compete with Intel and others for market share. I think this bears watching..
I think Broadcom is the front-runner here. The company has admitted they are lagging the competition in apps processors and haven't really communicated a roadmap. And we all know how aggressive Broadcom is with M&A. Broadcom could integrate OMAP with its baseband and other connectivity solutions while leveraging its position with leaders like Apple.
The only way this makes any sense is if the TI board has decided that becoming a pure play analog company is the best long term growth strategy. The acquisition of National supports this and Analog is a very high margin business with less volatility than selling processors. It takes an army of software developers to compete in processors these days and that drives down margins. However I doubt this is more than speculation, a move like this would cut off a lot of TI's growth potential and where would it leave their DSP and MSP430 businesses?