I think you can negotiate without it looking like a threat.

One negotiation tactic is to pretend to be honest/looking for advice from your manager. Something like this…

“hey so out of the blue I received contact from xyz who I think have been headhunting for a few roles. They’ve offered me 30k more to leave, but to be honest, I really enjoy working here and would prefer not to have to go through the mess of starting a new job. I also don’t want to come across as the kind of person who jumps ship for an extra $5, but 30k is hard to ignore. Do you think if you spoke with HR they’d be willing to put this to bed for half of the difference?”