I think this question might be dismissed very easily, but I'd like to try to provoke a sort of blurring-the-lines idea that may be interesting.
I'll start by putting two definitions here, the first of "Knowledge" from Wikipedia, the second of "Empirical" from Google (Oxford English pocket dictionary).
Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts, information, descriptions, or skills, which is acquired through experience or education by perceiving, discovering, or learning.
based on, concerned with, or verifiable by observation or experience rather than theory or pure logic.
So, quite basically it seems obvious that the distinction between empirical and non-empirical knowledge would be the distinction between "experience" (or, a postriori) and "theory" (or, a priori). Contra to this common position, I'd like to ask whether we should really consider the "theoretical" ideas as "non-empirical".
First, let's look at what "Empirical" focuses on: "Experience". Now, surely experience mostly refers to some external interference with the subject (from the Wikipedia page: "Experience is the knowledge or mastery of an event or subject gained through involvement in or exposure to it. Terms in philosophy such as "empirical knowledge" or "a posteriori knowledge" are used to refer to knowledge based on experience"). But let's not forget that experience doesn't involve only this kind of interference; it may also involve an intrinsic interference of oneself within itself, as suggested by the "mental" experience part of the Wikipedia article:
Mental experience involves the aspect of intellect and consciousness experienced as combinations of thought, perception, memory, emotion, will and imagination, including all unconscious cognitive processes.
From here, there are two options to proceed:
Exclude "mental", or any intrinsic sort of "experience" from the term "Experience" (another option is to exclude it from the term "Empirical"). But here we'll need to work a bit harder on defining which parts of experience are to be considered intrinsic (or, which parts of experience are to be considered empirical). We might rephrase and call the distinction of empirical and non-empirical as "external" and "internal" knowledge.
Redefine the term "Knowledge" (or "Empirical") to erase the clear distinction between "experience" and "theory". Thus leaving us with only one sort of "Knowledge", which may include all sorts of experiences, externals and internals.
If we take upon the first choice, we can happily return to our distinction between empirical and non-empirical knowledge, while noting in our minds that we may have made an artifical, possibly flawed divide of experiences.
On the other hand, if we take upon the second choice, we lose the empirical and non-empirical distinction, and might sometimes muddle our considerations and studies of knowledge by including types of knowledge we wouldn't want to include, thus making us either come up again with a distinction, maybe a more pluralistic one, or a more detailed one, or simply accepting our inability to distinct the sorts of experiences forcefully and reach theories that would include and consider all of them altogether.
So eventually, summing it all up (quite unfairly), my question would be where does "Knowledge" and "Empirical", in all their meanings, converge? I suggested that they ultimately converge in every way possible. I'd love to hear different opinions.
Note: my knowledge of epistemology is fairy limited, so all of this may be just a big nonsense. If so, comment below and I'll delete the question.