It came to my attention that even though squibs can't cast spells, they can work in a magical environment and they can see magical creatures.
My question is then, considering (so far as we know) that brewing potions doesn't actively involve using magic, with the right instructions, ingredients, tools and a fire could a squib become a potion master?
No, a squib (or a muggle) cannot brew a potion.
As revealed in the latest update on Pottermore, although potion-making doesn't appear to have a great deal of magical input, the reality is that at some point in the process wandwork is essential to add magic to the ingredients.
"It is often asked whether a Muggle could create a magic potion, given a Potions book and the right ingredients. The answer, unfortunately, is no. There is always some element of wandwork necessary to make a potion (merely adding dead flies and asphodel to a pot hanging over a fire will give you nothing but nasty-tasting, not to mention poisonous, soup)."
Since a squib is incapable of performing wanded magic, they would also, by definition be incapable of brewing a working magical potion.
This was backed up in an interview in 2006, albeit one largely focused on muggles rather than squibs:
Q: Can muggles brew potions if they follow the exact instructions and they have all of the ingredients?
JKR: Well, I'd have to say no, because there is always...there are magical component in the potion, not just the ingredients. So, at some point they will have to use a wand. I've been asked what would happen if a Muggle picked up a magic wand in my world, and the answer would probably be something accidental... possibly quite violent. Because wands, in my world, is merely a vehicle, a vessel for what lies inside the person. There is a very close relationship -- as you know -- between the wand that each wizard uses and themselves. In fact, we'll find out more about that in book 7.
For a muggle you need the ability, in other words, to make these things work properly but you're right and I think that's an interesting point. Potions seems, on the face of it, to be the most Muggle-friendly subject. But there does come a point in which you need do more than stir.
The question still remains whether a squib or a muggle could assemble previously magicked potion components and combine them into a working potion but the overall impression seems to be no, they could not.
