How well do Aragorn and Saruman know each other?

Question

In the chapter Flotsam and Jetsam in the The Two Towers, Aragorn has this to say of Saruman:

‘Once he was as great as his fame made him. His knowledge was deep, his thought was subtle, and his hands marvellously skilled; and he had a power over the minds of others. The wise he could persuade, and the smaller folk he could daunt. That power he certainly still keeps. There are not many in Middle-earth that I should say were safe, if they were left alone to talk with him, even now when he has suffered a defeat. Gandalf, Elrond, and Galadriel, perhaps, now that his wickedness has been laid bare, but very few others.’

This indicates that Aragorn was fully aware of the abilities and nature of Saruman. Was this information second hand via Gandalf/Elrond or is there in any work indications that they had crossed paths previously?

We know Aragorn has never been to Isengard:

I have never been in Isengard, but I have journeyed in this land, and I know well the empty countries that lie between Rohan and the Shire.

But that doesn't exclude the possibility that they met elsewhere.

How well do Aragorn and Saruman know each other personally, had they ever met or had dealings prior to the attack on Rohan?

Answer 1

I'm not aware of any canonical mention. But note that Aragorn, in his guise as Thorongil, served under King Thengel of Rohan for many years. It is at least plausible that Saruman would have visited Edoras during that time, especially given that he posed as a friend to Rohan originally.

Answer 2

They at least knew of each other

While there is no recorded meeting of Aragorn and Saruman before the War of the Ring, Aragorn was a confidant of Gandalf and Elrond and would have at least have heard a lot about Saruman.

When Aragorn was young, he traveled in the south and served in Rohan and Gondor under the assumed name of Thorongil ("the Eagle of the Star"). At this stage he had heard enough to advise Ecthelion (the father of Denethor) to trust Gandalf rather than Saruman.

Thorongil often warned Ecthelion not to put trust in Saruman the White in Isengard, but to welcome rather Gandalf the Grey.

_{The Lord of the Rings Appendix A I (iv) Gondor and the Heirs of Anárion}

When Aragorn joins Gandalf, Théoden and others in the parley with Saruman after the Battle of Helm's Deep. Saruman recognises Gandalf and Théoden, but not Aragorn.

‘But come now,’ said the soft voice. ‘Two at least of you I know by name. Gandalf I know too well to have much hope that he seeks help or counsel here. But you, Théoden Lord of the Mark of Rohan, are declared by your noble devices, and still more by the fair countenance of the House of Eorl.

_{The Lord of the Rings Book Three, Chapter 10: The Voice of Saruman}

However, when Argaorn tells Gimli and Legolas what happened when he looked in the Palantír, he suggests that Saruman might have recognised him if he wasn't dressed like the Rohirrim.

To know that I lived and walked the earth was a blow to his heart, I deem; for he knew it not till now. The eyes in Orthanc did not see through the armour of Théoden; but Sauron has not forgotten Isildur and the sword of Elendil.

_{The Lord of the Rings Book Five, Chapter 2: The Passing of the Grey Company}

That quote is the closest I can find to evidence that Aragorn and Saruman had met, but it is clear that they knew a lot about each other.