I work in a very specialized area within healthcare. There are only a few competitors in our area, and one of them has reached out to me directly (the hiring manager, not HR) about an open position they have. The department director saved my resume from another posting a few months ago and shared it with this manager, thinking I'd be a good fit.
At my current organization, I've been repeatedly told how valuable I am to this department. I have a good relationship with my boss. I've asked for a position like the one this competitor has open, and I'm told "we want to put you in that position, but it takes time". It's been months, and there's no movement. I'm going to discuss the opportunity with this competitor, because it's the position I've been looking for. However, if my current employer offered me something similar, I'd stay because I like my team.
Do I tell my employer I've been reached out to by this competitor in the hopes it speeds them along if they're actually considering giving me that position? When do I tell them (now, after interview, if I get an official offer)?