There were a few voices in those cultures who thought slavery was unjust or even 'contrary to nature', but even they had no plans or proposals to abolish slavery. I can recommend some earlier answers:

• Here you can read about the examples we have have of anti-slavery sentiment, as written by u/secessionisillegal
• Here is a discussion with a short answer by u/captainhaddock and comments by some others on the issue, with a few examples from outside the Mediterranean as well
• Here the user u/colorfulpony has written about how Christians in the Roman Empire viewed slavery

The short answer would be no, or at least, if there were any anti-slavery sentiments we don't know about it. I'll try and discuss ancient attidudes slavery in this answer. But broadly, there is nothing in the sources we have to indicate any kind of movement to eradicate the institution of slavery in the Ancient world.

The first thing to note is that all the texts we have relating to slavery were written by elites. I'll go through a few of the canonical authors of the Ancient world (Plato, Aristotle, Cicero etc.) and try to explain why I think they illustrate a lack of anti-slavery sentiment, often instead making an effort to explicitiy justifiy slavery. All we can do, in terms of trying to find anti-slavery sentiments, is try and read against the grain to discover if the attitudes expressed in these texts is universal, or if there might be some opposition implied within them from other people. Also, I'll only be discussing Greece and Rome, mostly because that's all I feel qualified to discuss, but also because they are the only two genuine ancient slave societies. Furthermore, Greece and Rome are salient in these discussions. Generally, we can distinguish between socitiets with slaves and slavery, and slave societies. Classical Greece, especially Athens and Sparta, and both Republican and Imperial Rome were genuine slave societies: large sectors (up to 50%) of their population were made up of slaves, and the polity would have collapsed without them. It's interesting, although perhaps tangential, that it is these societies from which stem many of our ancient sources and these socities which are so integral to the western tradition at large. Other societies in the ancient world, I can see have been discussed in other answers to this post, but they also lacked a slave system as widespread as the ones found in Classical Greece and Rome.

So, ancient Athens. Again, not much opposition to slavery can be found. Scholars have debated whether there was slavery in Plato's Republic. It had been argued that the lack of explicit mention of slaves in the ideal society Plato outlines implies his opposition to the institution of slavery. In counternance to this Gregory Vlastos wrote a fairly convincing article titled 'Does Slavery Exist in Plato's Republic' claiming two things. A) There is explicit mention of slavery in the Republic although its discussion is sparse B) The sparse discussion of slavery actually implies Plato approves of Slavery. As a rough rule, if Plato discussed it, he thought it needed changing, and his proposed republic changed a lot of things. The lack of discussion probably meant he thought slavery was perfectly justified. I'm inclined to agree with both these arguments

Let's move on to Aristotle. Aristotle, is the most pro-slavery out of all 3 authors I'm discussing. He famously outlined his thesis on the natural slave, which amounts to a justification of the enslavement of all non-greek people. He does however, hint at the opposition of others to his own idea of natural slavery. He sets out to write his theory of natural slavery in the Politics to argue against those who said man could not be a slave by nature. There is an implication there, that somebody opposed the idea of natural slavery, and Aristotle felt it necessary to refute this positon right at the outside of the Politics. However, opposition to natural slavery doesn't imply opposition to slavery itself. You could still believe the institution legal and legitimate even if you didn't think any humans were born slavish. So again, not necessarily any implication of opposition to slavery.

Jumping forward to the Roman world, again little to no opposition is found. Cicero discusses slavery in Of Duties but mostly to stress how you ought to treat slaves well. Again this doesn't imply any opposition to the institution itself, just an idea that slaves deserved some basic decencies. The only other major opposition to slavery would probably be the slave rebellions, the most famous being led by Spartacus, however it's unclear whether they wanted to abolish slavery, or just emancipate themselves. Which leads us back to a key point, all of our ancient sources suggest little to no opposition to slavery, they were all also written by elites who benefitted from an almost total relief of labouring duties by the practice of slavery. Who knows if their beliefs were widespread, or if there is some lost and forgotten opposition to slavery. My own hunch would be the former, that elite views reflected that of society at large and slavery was probably widely accepted without opposition. Althought continual attempts to justify slavery might imply opposition, I think that surely something would come through the source record about explicit opposition to slavery, even if the author stood in contrary to the position

Ancient people had no problem with the idea of slavery. Similarly, early modern Europeans had little to no opposition to slavery. Abolitionism, it would seem, is a product of the Enlightenment and Protestant Evangelicalism, both of which stem from the 17th and 18th centuries. I hope this answer helps, feel free to comment if you have any follow up questions.