What is the best way to collaborate with a professor whose current work one is extending?
What should my best course of action to collaborate with him? (He is a very high profile professor)


Your best course of action is to email him, explain the work you've been doing, and politely suggest exploring the possibility of a collaboration. However, you need to seriously work on your mindset before writing the email, because right now I feel like the reasons you are interested in the collaboration are not good reasons - you seem to be interested in the reputational benefit of having him as a coauthor and in the fact that if he is a coauthor then he can't be the referee for the paper; in other words, your collaboration offer will not be based on a genuine interest in the intellectual contribution this "high profile" professor can make to the work, and therefore I would say it is not being made in good faith. If I were the professor and got wind of what your motives are (and it may not be so easy for you to hide them, even if you try to phrase the email dishonestly, which in any case I would not recommend doing), I would not only refuse to work with you but would also develop a poor opinion of you that could be long-lasting and would be hard for you to correct.

To summarize, you are putting the cart before the horse here. You should contact the professor if and only if you are genuinely and in good faith interested in an intellectual collaboration rather than a mere formal coauthorship. Even then, keep in mind the professor may refuse your offer, because he is busy or for any number of other reasons (or for no reason at all). Your offer should be phrased in a tactful way that leaves your dignity (and any potential interaction you may have with the professor in the future) intact in the event that he is not interested in your offer. Good luck!