I've been doing what I'm doing for a little over two years now. I got this position because I was doing tasks I liked and that seemed to be useful, so they made it my job. Over those two years I've answered every, "can you do this?" with a yes and my job slowly shifted to this project management work that I don't like.
Have you talked to your management team about what you do and don't enjoy about what you're currently doing, or inquired about opportunities to change things up or add/delete responsibilities with your job? Is there something you currently do that can be passed along to someone else on your team in order to free you up to learn something new? Sometimes talking the boss into stuff like that is all about how you frame it.
I think this is a good next step for me. I'm a Type 5 in this system called the enneagram and my basic fear is being useless, helpless, or incapable. Going to a manager and saying "this is a thing I can't do" just seems like the worst thing in the world. I'm taking baby steps by asking a bunch of internet people (hubski) and yesterday I brought it up with a small church group and asked them to hold me accountable, but I guess talking to management would be a good next step.
I have never heard of the enneagram system, but I suspect I may be a fellow 5. It is very difficult to say no to your manager, with my current one we have a good relationship and I can feel free to say no, sorry, can't right now, or okay then which of the other million priorities am I putting off for this? And I can be sarcastic about it too and we will laugh and most of the time I will probably still do all or part of the request anyway. Although sometimes I suggest an alternate method of getting her request completed and she goes for it. Damn I am gonna miss her when she retires. Anyway, my personal bet is that since you've shown yourself to be an effective employee and good at learning new things in the past, there's a good chance they will see it as a reasonable request.