"I could wager I know the face of the man I will marry better than either of you knows that of your future husband."
The Aes Sedai appeared regretful of having spoken. "Perhaps I only meant we share an ignorance. Do not read too much into a few words." She looked at Nynaeve consideringly. "Should I ever choose a man - should, I say - it will not be Lan. That much I will say."
This is before Rhuidean and the rings ter'angreal, so this knowledge could have come from the Aelfinn. Alternatively it could have come from a viewing by Min (for evidence, see the tEotW passage quoted by @DavidH in the comments), though I can't remember us ever seeing Min knowing about Moiraine and Thom in a Min-PoV chapter.
Just rereading the series from the beginning after reading AMoL. From Moiraine's discussion with Thom in TSR Ch. 17, we might infer at least two questions:
She has asked about her fate and the fate of her companions from her assertion that she can promise Thom that he will not die in Tanchico and that they will meet again because he will survive Tarabon (p. 245-246). Does she know how much later they will meet again at this point? Not sure, but such knowledge might help to stiffen her resolve about how she will deal with Lanfear after she goes through the rings in Rhuidean. Inferring the question was about more than Thom because she seems to know in a way that exceeds mere caution that Ny and El will need some help staying alive in Tanchico (and along the way back).
She asked about Owyn's circumstances. No evidence before or since that she had collected this info elsewhere. (Not that we ever get the answer...) I've looked at the phrasing carefully, and I don't think she's using sleight of tongue here to suggest she has info that she doesn't. Plus Thom perceives sympathy and regret from her, though he tries to deny it. This tracks with her knowing about this tragedy in her future sweetie's past.
Granted, these are inferences, but now that we know all we're going to get except info to be dropped in the forthcoming Encyclopedia, they fit the story. Moiraine has known about the doorframe for some time now. I can picture her formulating a first question with exact wording, and then having a path A/B/C for the other two depending on the answer to the first (as opposed to Mat's just blurting out what's on his mind at the time).