I am about to get my master's degree and have published a few papers in highly reputable computer science journals. I have gotten an "informal offer" for a PhD position from a world-class university. An informal offer here means that a well-funded professor has e-mailed me, strongly encouraging me to apply and to make sure to mention his/her name in the application so it gets routed to him/her.
For various reasons, I'm leaning towards not pursuing a PhD so I'm currently working on my resume. I'm wondering if it's a bad idea to mention anything about this informal offer in the personal letter. The professor making the offer will not be the one writing my letters of recommendation. Verifying the claim would not be hard, but it's not really a tangible accomplishment. On the other hand, why shouldn't I highlight the fact that I could get into the best graduate program in the world if I wanted to?