Is Varys a mermaid? No, of course not, that's ridiculous. He could be a merman though.
No wait, don't go! There's actually quite a bit of evidence to support this theory, as crazy as it sounds. There's plenty of evidence to suggest that merfolk - or merlings as they are called - exist in Westeros. Don't forget, this is already a land with zombies and dragons!
Characters in Lannisport and Oldtown claim to have seen merlings. Strange black oily stone can be found all over the world, remnants of some underwater civilisation. The Driftwood Throne of House Velaryon is said to have come from the Merlings, and the Greyjoy's Seastone Chair is made from the same mysterious black oily stone and is said to have been found already sitting on the Iron Islands when the first men set foot there. The legendary Winged Knight of the Vale is said to have had giants and merlings amongst his friends, and, well, we know that giants exist in Westeros.
So there's a lot of evidence that Merlings exist. But why is Varys a Merling?
There's a popular fan theory started by a chap called 'Nightflyer' (I assume that isn't his real name) that has been making the rounds that Varys is a Merling, and it's a convincing one.
Who is Varys? He's mysterious. We don't really know anything about him, or where he came from. All we do know is what he himself has told us. He's master of secrets, he is a fat eunuch... or is he?
Varys doesn't have a proper bed in his room. There's just a bed-shaped slab of stone that he uses as a secret passage. So... Where does he sleep? In the bath, presumably, unless merlings don't sleep.
Vary's smile is described as 'slimy'. He is bald, his body large and lumpy, almost fish-like.
In a Clash of Kings, Tyrion threatens to have Varys thrown off a ship. Varys resonds that he isn't worried about this at all, and that if Tyrion means to kill him by drowning him in the sea, then he's likey to be disappointed. Varys isn't worried about this death threat at all, for he would just swim away into the ocean.
"You might be disappointed by the result... I keep on paddling"
[ACOK, Tyrion IX]
Varys claims to be a eunuch, with no... bits down there. And of course, merfolk would have no bits down there either. This story dissuades anyone from wanting to check out his junk, as well as deflecting any suspicion from lack of relationships - the perfect cover for a merman who is unable to procreate with humans.
And of course, what if his story about being made a eunuch was genuine? After all, it happened in MYR, a clue if ever there was one. Varys claims his manhood was taken from him... and maybe that is literally true. Maybe the sorcerer took away his manhood, magically transforming him into a merman?
Varys' body is large and he wears long flowing robes. It is the perfect disguise with which to hide a lower aquatic body. We've never seen Varys's feet just the bottom of his robes as he glides along the ground.
Who is Vary's ally? Illyrio. Also described as a big, fat man who wears robes that cover his lower half. Also from Myr.
In A Game of Thrones when Arya overhears Varys and Illyrio plotting, something very interesting occurs. How do they get in and out of the underground catacomb? Via a well!
"The man with the torch pushed at something. Arya heard a deep rumbling. A huge slab of rock, red in the torchlight, slid down out of the ceiling with a resounding crash that almost made her cry out. Where the entry to the well had been was nothing but stone, solid and unbroken"
[AGOT, Arya III]
If Varys and Illyario are both so big and fat, why do they go to talk in a difficult to access location... unless it is easy to access for merfolk. The only way out for Arya is to swim via the sewers and out into the nearby river. There's a whole network of waterways under King's Landing. What is difficult for a human to do is simple for a merman.
So Varys and Illyario are both Merfolk from Myr. Is anyone else in on this? Well, don't forget Lord Manderly, a huge fat man with a taste for human flesh. What's his sigil? Oh, it's a merling! Hiding in plain sight indeed.
And what of Littlefinger. He claims to have some sort of hold over Varys, but he's not a big fat man, he can't possibly be a Merling. Or can he? After all, his ship is called the Merling King, and he comes from the Vale, where as we see there have been Merling incurions in the past.
What is Varys's endgame though? He's thrown his lot in with the Targaryens. He and Illyario have supplied Dany with dragon eggs, putting themselves firmly on the side of fire, against the coming winter. But when summer comes, the ice must melt. Does Varys plan on using the dragons to melt the Wall and so flood Westeros to create more living space for the Merlings and a supply of dead humans for them to feast upon?
After all, once the sea level rises, very few places will be habitable by men. Only a few high places. Such as the Eyrie. Where Littlefinger now rules.
Littlefinger, the Merling King.
Further Reading: Original forum post where the theory began (via web.archive)