People did not directly associate rats with the plague. The most common explanations were based off miasmatic theory and humoralism, as was - more or less - state of the art for mid-14th century medicine. (This assessment of the Paris medical faculty from 1348 primarily blames miasmatic airs caused by certain astronomic configurations: https://archive.org/stream/derschwarzetodin00hoen#page/152/mode/2up)

However, people generally saw rats as vermin and cities tried to cull rat populations, although this was probably primarily to keep them from polluting/feeding on food storages. If you take a look at police ordinances of that time, most cities employed at least one person to deal with stray animals and animal carcasses, including rats (Interestingly, if you take a look at Kunz Has' Nuremberg Encomium, this basic service had developed into something you could almost call an organised attempt at city cleaning by the end of the 15th century). Any effect this may have had on actually preventing outbreaks of disease is conicidental, much like many cities instituting quarantines - and other similarly sensible measures - without people really understanding why these measures worked.

Beyond this, I am not aware of any sources that show anything more than the passing awareness for rats you can find in police ordinances. So the answer to your question is probably "somewhere between possibility 2 and 3": they were common enough - and seen as a nuisance - that town councils adopted measures, but their relative absence from (non-scientific) sources beyond that indicates that they were situated somewhere on the fringes of people's awareness.

If you are interested in contemporary views on the origins of the Black Death, I recommend Bollox' book (where you'll also find a partial translation of the Paris assessment). It contains a nice and representative array of (excerpts from) contemporary sources in translation, including the most popular explanations competing with the scientific explanations, namely: "it's the End Times/God's Wrath/because we are all sinners" and the ever-popular "it's the Jews' fault!".

Source:

Horrox, Rosemary, The Black Death, (Manchester: Manchester UP, 1994).