Should I Coach the CEO I Have a Contract With

I have been offered a coaching contract opportunity with a consulting company. I will be coaching the company’s clients to reach their desired goals after an assessment has been performed to let them know where they currently are relative to where they want to be.

However, I am considering offering to coach the CEO of the company that I am contracting with. I am considering this offer because he says he would like to have someone to bounce ideas off of and discuss plans that he may have for his company. This sounds like an opportunity for coaching to me, but does this sound like an offer that I should make?

When I ask myself that question, what comes up is ‘why not?’. I can’t come up with a good reason not to, but I’m wondering is there a side I’m not considering from a business perspective. Thank you for your insight.