If management get the idea that you're thinking about leaving, then they'll either seek to talk about it and see if you're happy (if they really want to retain you), or they'll side track you away from anything interesting, or just stary freezing you out.
Lead the "can you review my CV" conversation in the right way first to avoid the obvious question, and hopefully mitigate any blow-back.
Hi Mike, I've not updated my CV in years, so I just took it out and dusted it off. Can you take a read through and see if it looks ok to you? I'm not looking for anything right now, I just wanted to keep it up to date in case I forget anything....
Then offer him a drink. Or something.
Whether you ask or not depends on whether you think that Mike will talk about this to your manager/lead or not. Sometimes colleagues are trustworthy.