Did Saber recognize Illyasviel in Fate/Stay Night?

Question

In Fate Zero, Saber doesn't exactly meet Illyasviel, but she does see her, which is hard to forget because she looks pretty much exactly as her mother Irisviel, who was a good friend of Saber's.

In Fate Stay Night, Saber runs into Illyasviel multiple times, and eventually Illyasviel ends up living with her in Shirou's house. But, as far as I'm concerned, Saber doesn't seem to "react" at all. By this I mean something like:

• "Oh boy, that's Illyasviel, damned Kiritusugu's daughter"
• "Whoa, she looks exactly like my good old friend Irisviel"
• "von Einzbern? That rings a bell"

But it doesn't seem (to me) that Saber actually realizes this.

Does Saber recognize Illyasviel? If yes, why doesn't she bring it up?

Answer 1

Yes, Saber's (Arthuria) situation as a Servant is unique. She is not a true heroic spirit, but rather an incomplete one (See: Fate/Zero novel, Vol. 2, Act 5, Part 1):

As Saber - that is, Arturia - is an incomplete Heroic Spirit, she would not possess the knowledge that surpasses time and space one gains when one has reached the Throne of Heroes.

According to the Type Moon Wiki:

Heroic Spirits are those who have been removed from the time axis and placed on the Throne of Heroes, while Saber can still be considered living. The hero known as King Arthur is not currently classified as a Heroic Spirit, so she cannot be called a complete Servant. She made a pact with the World as she was on the verge of death after the Battle of Camlann that will require her to become a Counter Guardian, a subcategory of a Heroic Spirit at the service of the World, after her death. These pacts are normally done by those requiring the power beyond ordinary humans to become heroes during their lifetimes, but her wish instead came at the time of her death because King Arthur did not require support to become a hero.

Having technically not died yet, Saber cannot take on Spirit Form like most other servants because she's technically still considered alive. This allows her to keep all memories of her search for the Grail, unlike Heroic Spirits don't keep their memories in order to prevent inconsistencies.

With that being said she most likely realizes the positions she is in and the recurring characters, but does not act upon it would complicate matters (singling her out as an irregularity, raise unnecessarily questions that may distract her master).

Answer 2

Saber recognized that Illya was a homunculus created by the Einzberns like Irisviel however Saber was never told Illya's name and assumed that Illya would grow normally during the ten years between Holy Grail War's so when Illya introduced herself Saber thought Illya was too young to be Irisviel's daughter.

Answer 3

If you pay close attention to Fate/stay night: UBW, you may be able to tell that Saber recognizes Illyasviel.

When Illya first introduces herself, she says "Von Einsburn. Sounds familiar, Rin?" After she says that, Saber tilts her head down and sighs as if she is remembering something she doesn't want to think about. Though this evidence still leaves much to be desired, Saber has never been one to submit to her feelings and often keeps them concealed within. Therefore, she wouldn't likely say, "Oh my god. You're Irisviel's daughter." even if they were alone together especially because I'd imagine that Illya reminds Saber too much of Irisviel, who is dead.

Honestly, if I were saber, I'd be acting the same way if I were in such a situation.