I currently have a full time job that is going well, but beginning to stagnate. I received an offer for another job that I'm very interested in, but still unsure if it's the right time to move on.
Is there any benefit to sharing this information with my current manager? We have a good relationship, but not sure if I should put this on his radar.
Short answer: No, unless you intend to ask for a counter offer.
Now is decision time for you, you can either accept the offer and move, or reject the offer and stay where you are. Telling your manager of this classifies you as a "flight risk", and a risk to whatever projects you are working on.
So no, I would not tell him unless I had already decided to accept the other offer and give your notice.
No, but you can talk to your manager about ways to improve your current job.
Since you are "unsure if it's the right time to move on" but the job is "beginning to stagnate", it sounds you should talk to your manager about how your job could be changed to avoid that stagnation. Perhaps you could ask for a promotion, raise, or a change of duties so that your current job is just as interesting as the new job. If your manager is unable to improve your current job now, then it sounds like it's time to take the new job.
It really depends on your relationship with your manager. Usually the answer is no. But if you have a very good relationship AND you've seen your manager react well when others have given a heads-up, then the answer could be yes.
Some questions to ask: what do you hope to gain by telling your manager? Professional courtesy of giving them more warning is good, if you have seen they take that well. Perhaps there are other options at the company you are at, and your manager might like the option of helping you grow, rather than your current stagnation? If you think those questions would have positive answers, then it could be worth talking to the manager.
