Baby monitors often use the same frequency wireless so wireless networking per se may not be viable.
Does the room contain a working ethernet jack? What is the distance between the room and the monitoring location?
Do you need to monitor the audio via some existing network device or is just a microphone on the resident's end and a speaker on the monitoring end all that is needed (i.e., listen only versus intercom).
Is there any concern that the resident may unplug or otherwise disturb the microphone either intentionally or otherwise?
I googled "microphone over ethernet" along with some variations of the words and phrasing.
I excluded wired camera/microphones for the obvious security and privacy concerns but if the camera can be truly disabled then such a system may be acceptable. I do not know your full environment.
Here are a couple of examples of what I found:
https://www.monoprice.com/Product?p_id=3597&gclid=CJKL6J2G49ICFVxLDQodoI0IPQ
http://www.markertek.com/product/mux-500028-2pk/muxlab-500028-rca-stereo-audio-hi-fi-balun-2-pack
There are other similar links and products.
Should be quite doable - just not totally sure about the full extent of any constraints that may exist or to what extent you can "be creative" in setting up the necessary audio connectivity.