Who are Littlefinger's 3 queens?

Two of them are almost certainly Cersei and Margaery. The third is trickier however, and I think we're not necessarily meant to know who it is exactly. I can see the case for Myrcella as Dorne's puppet queen, Dany as a queen bent on retaking Westeros, and Sansa, whom Littlefinger seems intent on making a puppet queen in the North. It could plausibly be any one of those three women.

I just considered all the possible queens during and after the War of the Five Kings. The two queens who are definitely mentioned are: Cersei Baratheon Margaery Tyrell They're already pretty much at odds. The third queen however is quite tricky. The Queens in the North, Jeyne Westerling and Sansa Stark - I doubt Jeyne has any real power now, and I don't see Sansa occupying Winterfell anytime soon. The Queens in the Iron Islands, Alannys Harlaw and Asha Greyjoy - it's safe to rule both of them out, considering their current predicament The Queen at the Wall, Selyse Florent - Another one to be ruled out easily, as she hasn't really been a power player so far. Her greatest achievement is probably introducing Melisandre to Stannis. The Queens in Dorne, Myrcella Baratheon and Arianne Martell - Arianne with the alliance to Aegon, and Myrcella being crowned at Dorne. From Littlefinger's point of view, it's safe to leave out Arianne. Myrcella, I am not so sure. For the following reason. The Queen of Meereen, Daenerys Targaryen. She seems to be the most likely candidate, but, how well-informed is Littlefinger about the stories from Essos? There's also Maggy the Frog's prophecy The old woman was not done with her, however. “Gold shall be their crowns and gold their shrouds,” she said. “And when your tears have drowned you, the valonqar shall wrap his hands about your pale white throat and choke the life from you.” According to the prophecy, it appears that Myrcella is going to be crowned, and she'll die before Cersei. How true it is, we don't know yet. But it is certain that Littlefinger doesn't know about the prophecy. Though it's likely he knows something about Arianne about to crown Myrcella. (There's also the events of A Dance with Dragons to consider) This answer is getting really incoherent, and I'll edit it sometime soon. But to conclude, I'd say the third queen is most likely Daenerys, but it's really hard to rule out Myrcella.

Petyr Baelish sure loves to brag when he's with Sansa. She may be the only person whose opinion Littlefinger cares about, although he doesn't think much of her opinions. But oh boy, does he boast. Puffing himself up, you'd think he's Lann the Clever. So. Queens. Which ones. Five kings to three queens. There's five candidates who stand out - Cersei, Margaery, Daenerys, Sansa and Myrcella. He had a hand in Cersei being Queen. Or more accurately, in Cersei staying Queen. He definitely arranged Margaery becoming Queen. Littlefinger can't take credit for Daenerys or Myrcella. They're still other people's plays. Or misplays. That leaves Sansa. "Three queens?" She did not understand. Nor did Petyr choose to explain. Instead, he smiled and said, "I have brought my sweet girl back a gift." A very wicked smile, I'm assuming. Sansa amuses him.

The three queens are Margaery Tyrell, Cersei Lannister and Danearys Stormborn of the house Targaryen.The war of the five kings was over the moment Grey Winds head was sewn onto Robb Starks body.This was a more conventional war but the war of three queens that is a little different.Cersei and Margaery are vying for control of King Tommen and Dany. Well Dany is still trying to get to westeros and she is further from her goal then she has been at any other point I the series.

“You would not believe half of what is happening in King’s  Landing, sweetling. Cersei stumbles from one idiocy to the next, helped  along by her council of the deaf, the dim, and the blind. I always  anticipated that she would beggar the realm and destroy herself, but I  never expected she would do it quite so fast. It is quite  vexing. I had hoped to have four or five quiet years to plant some seeds  and allow some fruits to ripen, but now… it is a good thing that I  thrive on chaos. What little peace and order the five kings left us will  not long survive the three queens, I fear.”  â€œThree queens?” She did not understand.  Nor did Petyr choose to explain. Now, for most of us it is pretty clear that two of those queens are Cersei and Margaery as they have been playing their cards from quite some time. For the 3rd position we have a competition. It could be Ollena Martell (the Queen of thorns), but she is on the side of Margaery, so we can rule her out. there are other options possibly on his radar, like Asha Greyjoy  (would-be queen of the Iron Islands), Selyse Florent (Stannis’s queen),  or Melisandre (Stannis’s “true queen”). That Leaves us with two major candidates, Sansa and Danerys. But just after Petyr mentioned the 3 queens he starts talking about the betrothal to the future Lord of the Vale that he had arranged for her (in the books), it doesn’t seem like he’s thinking of her as a queen. Though queen of Westeros is quite possibly his final plan for Sansa — but since he says peace and order won’t survive the  three queens, that seems like a contradiction to his usual “everyone  will love you” approach with her. Dany has a strong claim too. News of her expansion and dragons have reached Westeros and she has the Targaryen connect too. But I have always felt that in the coming times, there will be a 2 tier war in a song of ice and fire, the eternal war where Dany will fight with her dragons against "The Great other" and the game of the mere mortals where the 3 queen will bite their nails. So who are these 3 queens, one could only speculate. For what we know, he might be lying (so that Sansa feels like a queen), he surely has the reputation for that.

I think it's Cersei Margaery and Dany.  The last I'm not sure of but the "five kings" is in reference to the "war" of five kings, and Petyr seems to be predicting a full-out war's about to start up again.  If Dany comes to Westeros, it's Cersei and Margaery, not Tommen, who hold the reins to fight her back.  That would actually be kind of a fun twist, Cersei and Margaery allying against Dany after everything between them.  I don't really see it happening but one never knows.

It can be Olenna Tyrell, the Queen of thorns. A woman whose collaboration with Littlefinger bore fruit on the very day of the purple wedding.