Nope. Do not do that ever.

within my best interest to let him know What, specifically, do you hope to gain by telling him?

Folks, please don't use the downvote button as "No" button. This is a good question. A lot of people are tempted to tell their boss that they want to leave the job. The answers here show why that is a bad idea. The OP should not be penalized for asking a useful question, just because he doesn't know the answer already.

I did this once and it turned out okay. That said, I agree with the 'no' answers here, there is no upside for you.

Try the reverse situationist "he (manager) should feel comfortable letting you know if you are to be let go/fired". Do you think you manager would divulge anything?

You should always be a bit suspicious of people who tell you "you can trust me", because if you could, they probably wouldn't have to tell you that. Especially for people you've known for a while.

What they are actually saying is "if you're unhappy please tell me, and why". That's a more reasonable thing to say (although still to be treated cautiously)

At my current place, people have been given pay rises and new roles within the company when they've threatened/mentioned they may leave. It's not always a bad thing to be able to say 'ok, this is no longer what I want to do'. - That said, you need to be sure you're happy with them letting you go, if you do so (as they may lay you off there and then, depending on the legalities).

The answers below give a good overview of things to consider, but one thing they seem to leave out and which Erik's comment touches on is that given the high stakes involved, you can't just take your manager at his word here. All sorts of employers say a variation of this to their employees but good managers will actually have shown that they deal with people leaving or giving notice correctly. You can only base your decision to share this info on how your management handled situations like this in the past, not on vague promises or expressions of trust.

I learned my lesson on this in college. I asked my boss for more responsibility, he said "no", I told him I was going to find somewhere else that they would give it to me. Within weeks, my replacement was hired and I had until the end of the semester to train him. Fortunately for me, my replacement's incompetence was well documented within our ticketing system, so he actually was asked to leave and I got to stay. I, however, took the lesson to heart. Your boss, no matter how nice a guy he is is looking out for (in order) #1) himself, #2) the company, #842,193) you.

Please tell us what country you are in? In countries with good employment laws this is far less risky than in countries where they can fire you on a whim. In most (all?) EU countries, firing you for saying you intend to leave would be illegal and you'd easily win a tribunal against the company.

Its a Trap

What is the point of telling him?

You gain nothing by telling and you stand to lose a lot. Never trust HR or your management when it comes to stuff like this.

I don't have the reputation to answer. However I've done precisely this on a couple of occasions, though not in those exact words. One manager asked me to stay to a set date if possible to finish a project. No problem there. Another one convinced me that I could leave the country and retain employment. I feel like its worked out well for me. That's not the same as recommending it.

@Erik, why is it "Especially if you've known the person for a while"? Does knowing person for a longer time make it a reason to trust them less?

@Dennis no, if you know someone for a while then you should already know whether or not they are trustworthy. If you have been working with someone for 3 years and they STILL need to tell you that you can trust them, then something is off. That should have gone without saying, unless you cannot in fact trust them.

Well, he's going to find out when you hand him your resignation anyway, so sure.

"I wonder ... if it would be ... within my best interest to let him know." What possible upside do you see in telling him?

I think the desired upside is that the boss will help fix any conditions that are in the way of continuing the employment at the company. Boss cannot always fix company culture or politics, but sometimes can help with salary, benefit negotiation, or task re-distribution, etc. In other words, my guess is that "potential loss of employee" is a negotiation tactics to help change something employee is not happy with, and here boss encourages you to use it.

Thank you all for the overwhelming support on this question. I came back to this and the detail in the answers have been great. I am also glad I wasn't the only one interested in this. I'll be honest I was a little afraid of asking this question but glad a lot of people were curious as well.

A manager who will give you an honest answer to this question is probably a manager who will already know that you're not satisfied. Honesty and awareness correlate closely here. If you think there's a chance you want to stay, tell your manager what you'd like to move towards and let them try to keep you.

Communicating that you are considering other opportunities can be used as leverage if he thinks you are particularly valuable and you have certain desires that can be met. But it can also backfire. This is just to say that it can be beneficial, but only if you approach the situation with a business mindset. If you get an offer you want to sign it may not be a bad idea discussing it with him before you sign it and seeing if he does something to keep you that you weren't expecting.

Work is not real life although it will effect your life. Business is war and Management has primarily one interest: protecting the interests of the company. So, Management is not your friend. Co-workers may be friendly but that doesn't mean they are your friends. If you need to share how you feel about your job talk to your family or trusted friends in your personal life. At work you need to watch what and how you speak so that you can manage impressions and thus influence the perceptions of your superiors, subordinates and co-workers to achieve your professional goals. Good-luck!

@Caleb I realize I never addressed your comment which is a good context. I feel the benefit would be he could give me a recommendation during my job search, as awkward as that may be. I don't have issues with finding other people to recommend me but I feel I have done good work under him and he can vouch for those things. Not sure if that sounds stupid or naive but that was what I thought could be a benefit. I'll update my question.