How to ask client toforward CV

Got a bit of a "problem"
Work in a front office markets role servicing clients (ignore wso title).
Recentely became a bit annoyed with the firm and trying to move somwhere else.
I work very closely with traders at funds/banks etc. and go entertaining with them all the time.

Now my issues: a job recently opened up at one of my clients firm that would perfectly fit what I am looking for.
My question, do I ask my client to forward my CV/recommend me or leave it? A bit scared that if I do ask him, it will negatively impact my business relationship with him.

Any advice would be appreciated, thanks!