External offer but interested in internal role

I have an external offer that is 20% more than my pay. I am torn on whether to take it. I want to try and negotiate and if they offer me more than I think I'll probably have to take it. The work isn't as interesting to me but the benefits and compensation and company are good.

But I recently saw an internal role on another team at my company that I really am interested in. I know multiple people on the project. I'm having an informal conversation with the hiring manager. If it goes well, I'm unsure how to approach the situation with the external offer timing. Do I tell my company that I have an external offer that I'm strongly considering but would love to stay if the process can be expedited?

This is a cost benefit analysis that only you can answer. You talk about the salary difference but also the benefits. How much better are the benefits? What about long term growth at both companies? If the work is boring how long will the extra salary keep you motivated? Do you know anyone at the next company or are you going in blind?

There's also something to say for you having comfort and status within the existing company. But if there's no chance for a big wage increase at your current company, maybe it is time to jump ship if that's a compelling factor.