There's a lot of important background information in order to answer the question quickly. I strongly suggest that readers who want to know the background information regarding Athenian democracy see this post by u/iphikrates. This will explain why we shouldn't imagine "voting rights" to mean going up to a ballot box, writing our preferred candidate on a piece of paper, and putting in the box. You, OP, might already be aware of this, but other readers might think that's what voting was in ancient Athens.

But the simple answer to your question is: not really. (I am going to answer from the point of view of the philosophers, although ancient Greek philosophy is a very broad category, so I'll just choose two cases of classical Greek philosophers who live in Athens.)

Some philosophers, such as Aristotle, believed that women and slaves lacked parts of the soul that would have made them good citizens. He says, specifically: "the slave has no deliberative faculty at all; the woman has, but it is without authority" (Politics I.13). The point is that slaves actually lack a whole part of the soul -- the part that lets them weigh their options and decide which ones are best -- but women have that part, but it doesn't have authority. What exactly this means is debated by scholars, but one possibility is that Aristotle is saying that women lack whatever non-slave men have that makes their reasoning not get trumped by their emotions.

Regarding slaves, Aristotle says: "There is in some cases a marked distinction between the two classes, rendering it expedient and right for the one to be slaves and the others to be masters: the one practicing obedience, the others exercising the authority and lordship which nature intended them to have. The abuse of this authority is injurious to both; for the interests of part and whole, of body and soul, are the same, and the slave is a part of the master, a living but separated part of his bodily frame. Hence, where the relation of master and slave between them is natural they are friends and have a common interest, but where it rests merely on law and force the reverse is true (Politics I.6).

The idea is that slaves are good at only being tools. Masters "look out" for the slave by replacing the part of their souls that deliberates, and slaves, in turn, serve their masters as tools.

So, Aristotle isn't exactly about to agitate for slaves or women to get more say in politics. In fact, he believes that women are best suited to ruling the household.

On the other hand, we have Plato. Now, we might think that the situation is different for Plato because he, in the Republic, takes the view opposite to Aristotle's: men and women have the same souls and therefore are capable of the same activities, including ruling.

Plato believes that not letting women be rulers would be wasting a valuable resource. Women are capable of the same activities and we want to tap into that resource for the sake of preserving the polis, so we ought to educate men and women the same way. This doesn't commit Plato to some radical equality: he does seem to think that women's bodies are worse than men's bodies, with the result that "all the pursuits of men are the pursuits of women also, but in all of them a woman is inferior to a man." (It isn't exactly clear what this means: are all women worse than the worst man, such that even the best women isn't as good as the worst man? Or maybe, it is that the average woman isn't as good as the average man? Or the best woman isn't as good as the best man?) And we could find other texts by Plato where he is clear that being born a woman isn't as good as being born a man.

The same goes for slaves. Plato, in fact, thinks that everyone has the same kind of soul. There isn't any room for people who are slaves by nature, like Aristotle thought. (The story gets a bit complicated when Plato considers less-than-ideal cities, like one he hypothetically constructs in the Laws. This state actually does have slaves, but we need to recall that they are indeed sub-optimal.)

But why didn't Plato agitate for women to get "voting rights" in ancient Athens, then? Well, because he didn't support ancient democracy at all. He offers sustained criticisms of Athenian democracy in the Republic and Statesman, and the core of his criticism in the latter probably gets at the heart of it the most concisely: Plato prefers rule by people with knowledge. He wants experts to be in charge -- specifically experts in matters such as justice and goodness and who know how to weave together the various components that make up a polis. The Statesman likens the ideal ruler to a weaver on several accounts. You don't solve any political problem by extending "voting rights" to someone without expert knowledge.