We know from Graendal's spy reports that Cyndane and Moghedien are the two trying to carry out Moridin's orders about Mat and Perrin.
It's then more a matter of guessing which is involved with whom, and we already know Moghedien is involved with Moridin's plot around Elayne in Andor, so... Cyndane seems the most likely suspect (though there's something to be said for a Lanfear vs. Elayne story, that's for sure. But I think Jordan isn't going this way, at least not now).

Moonhunter and Perrin have "unfinished business" since TDR (Min even told Perrin Lanfear was a danger to him), and Perrin and his wolves are "TAR foes" both worthy of a fight with her, and at the same time not so powerful in TAR that Lanfear would be turned into a non-threat (as might happen, if you have Cyndane or Moghedien vs. Egwene and the 4 WO face off early on. Jordan rather cleverly had Lanfear play TAR games with Egwene early, when Egwene was no threat, and with Rand and Perrin. Moghedien got involved with Elayne-Nynave (and indirectly Mat, in Ebou Dar - as he got involved with her two BA), and will likely return around Elayne soon. Neither Perrin nor Elayne are matches for Forsaken dreamers, but Egwene well might - might have no choice to be, anyway). It sounds possible Moridin will decide to send Cyndane (I expect Moghedien to die in TOM) against Egwene only once Mesaana gets herself killed. It won't be an infiltration thing, Cyndane will be sent for an assassination in TAR

Why is Cyndane playing games with Perrin? That was always Lanfear's style, to begin with. The only time she made a direct attack.... she was out of her mind, and she lost.

Then, she might have gotten directly involved (from afar still, it appears) under Moridin's orders. He never gave the order for the Forsaken to kill Mat and Perrin. He specifically ordered the Forsaken to have their followers kill Mat and Perrin. Unfortunate twists of fortune always caused the demise of the Forsaken when they tried to attack the three ta'veren. Moridin seems to have figured this out long ago.

My feeling is that Cyndane is now starting to play with Perrin's dreams herself because she's getting frustrated at the ineptitude of her DFs (who failed in Amadicia, the one time lately when Perrin was easy to reach ... someone must have tracked Perrin there, incidentally. Cyndane is one who can track ta'veren). Then, her plot to give Masema dream visions of Rand so he killed Perrin (he got Aram to do it. Masema was a coward) also failed, and Faile made sure Masema couldn't be used anymore. So it seems Cyndane.

From the scene in the prologue, I gather Perrin may already be either too powerful a dreamer or too well protected by the wolves, for Cyndane to attempt a straight assassination from TAR. Or by orders, she has to be cautious.

If any of this is true, it could mean there's no DF close enough to Perrin that Cyndane can use to kill him. She had to use Masema, and now she's a bit short on possible pawns and is getting involved more directly.

I think Jordan might have intended this storyline to raise the stakes of danger for TAR, before the LB begins. The world has become more and more dangerous, but for the moment, things have been totally stagnant in TAR since the apparition of Slayer in TSR (who isn't much of a threat there, as he clearly has not much talent to control TAR... he runs instead of disappearing, he's no good at hiding etc. He seems there "in the flesh" and not as a dreamwalker either), and the apparition of Moghedien, and the trap she made that Egwene escaped. There's been nothing more from the Shadow since... Perrin's story could be use to bolster the Shadow's "Dream Team" and their powers pre-TG, and make clear even a Dreamer of Egwene's stature can barely face their powers.

Of course, perhaps TAR won't at all be an important feature during TG, but it sounds unlikely.