No, a muggle absolutely cannot brew a potion.
As revealed 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 and that even adding magical ingredients to a mixture isn't sufficient to create a working potion.
"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
Since a muggle is incapable of performing wanded magic, they would by definition be incapable of brewing a magical potion.
As DVK has referenced in his answer, this information was already largely confirmed in an interview in 2006:
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.