While it may be impossible to prove that EVP is not paranormal. Current evidence suggests so.
Wikipedia has a comprehensive article on EVP with a list of natural explanations.
To just quote one
Auditory pareidolia is a situation created when the brain incorrectly interprets random patterns as being familiar patterns. In the case of EVP it could result in an observer interpreting random noise on an audio recording as being the familiar sound of a human voice. The propensity for an apparent voice heard in white noise recordings to be in a language understood well by those researching it, rather than in an unfamiliar language, has been cited as evidence of this, and a broad class of phenomena referred to by author Joe Banks as Rorschach Audio has been described as a global explanation for all manifestations of EVP.
There is another article on The Sceptics Dictionary
Perception is a very complex process, and when our brains try to find
patterns, they are guided in part by what we expect to hear. If you
are trying to hear your friend while conversing in a noisy room, your
brain automatically takes snippets of sound and compares them against
possible corresponding words, and guided by context, we can often
“hear” more clearly than the sound patterns reaching our ears could
account for. Indeed, it is relatively easy to demonstrate in a
psychology laboratory that people can readily come to hear “clearly”
even very muffled voices, so long as they have a printed version in
front of them that tells them what words are being spoken. The brain
puts together the visual cue and the auditory input, and we actually
“hear” what we are informed is being said, even though without that
information, we could discern nothing. Going one step further, and we
can demonstrate that people can clearly “hear” voices and words not
just in the context of muddled voices, but in a pattern of white
noise, a pattern in which there are no voices or words at all.
Given that we can routinely demonstrate this effect, it is only parsimonious to suggest that what people hear with EVP is also the
product of their own brains, and their expectations, rather than the
voices of the dearly departed. (Alcock 2004)
An article on wikisynergy (it seems old, half finished and with plenty of link rot) quotes David Federlein (a sound Engineer?) Emphasis mine again
Often EVP proponents have pointed to the fact that digital recordings
also pick up EVP as proof they are from beyond the grave. What is not
noted however is that the actual microphone recording to the digital
device is an analog piece of equipment subject to cross modulation in
cases of cheap engineering. Poor analog to digital converters,
fragmented ram, and faulty programming of lower quality digital
devices either compound a cross modulated source, or create new
splices of previous recordings added in to the new recordings.
Interestingly enough when EVP proponents are explaining how to capture
an EVP, often using high quality and properly grounded and shielded
equipment is discouraged in favor of cheap and low quality recorders.
While it is suggested to use a new tape every time (in the case of
tape recordings) the recorders themselves are low quality and often
inexpensive units that most likely are not up to the tolerance
standards of professional sound engineers. This seems to suggest that
EVP proponents may not understand the workings of radio broadcasting
and its effect on poorly engineered equipment all that well, and are
actually engaging in a controlled misuse of their electronics. Given
that there are billions of radio transmissions filling our airwaves a
device that is engineered poorly or has a faulty ground is almost
assuredly going to produce strange combinations of human voice
recordings that are somewhat mangled and in poor quality. Conversely
the very human need to hear what we want to when looking for meaning
in things would imply the physics of EVP alone is not to blame. Often
ghost hunters and EVP believers want to connect with someone as proof
of an afterlife, and may read into whatever recordings are captured
something that isn't there.
What about research?
An article CSI by James Alcock (the one referenced above) says
Serious parapsychologists today show virtually no interest in EVP, and modern reports in the parapsychological literature find no evidence of anything paranormal in such recordings.
and from the Sceptics Dictionary article
Despite widespread belief in EVP, scientists have shown about as much interest in the phenomenon as they have in John Oates's reverse speech theory, and probably for the same reason. We already understand priming and the power of suggestion. As Alcock says, the simplest explanation for EVP is that it is the product of our own wonderfully complex brain, aided by the strong emotional desire to make contact with the dead.
And noone so far has claimed the million dollar prize from the James Randi Foundation.
And of course there is fraud. An entry on the James Randi Forums lists a number of malicious hoaxers who need to be seriously investigated.