Here is my situation: A well-known senior researcher - let's call him Prof. Bigshot - wrote a paper. His paper is based on a good idea, but the implementation of that idea is shoddy (in my humble opinion) messy. After much thought, I, a lowly PhD student, cleaned up and extended the implementation and wrote a follow-up paper that improves the implementation of his idea and also extends it.
Both of our papers are publicly available on arxiv. I know (via gossip) that Bigshot's paper has been rejected twice already. I have not submitted my paper anywhere yet.
I believe his paper is being rejected because it is a conceptual paper without any meat. And I worry that my paper will also be rejected because it is incremental. However, if we merged our papers, I think it would be a strong paper as it would have both conceptual and technical contributions. Thus I think it would be mutually beneficial if we merged our papers. (My advisor concurs with this assessment. Merging papers is reasonably common in my field.)
How do I go about suggesting to Prof. Bigshot that we merge our papers? I don't know what the etiquette for this situation is. I worry that he will think I am trying to take credit for his idea. Should I just wait for him to bring it up? or should I actively suggest it?
I have interacted with Prof. Bigshot before and I also sent him a draft of my paper, to which he responded positively. So this is not coming out of the blue for him, but I need to be diplomatic nonetheless. In particular, I want him to feel comfortable saying no without anyone's feelings being hurt.