Saññā's definition

It is memorizing [sañjānana] to memorize again after [puna sañjānanapaccayanimittakaraṇa].
In path of purification, khandha-niddesa make summary from Sutta. Ma. Mū. Mahāvedallasuttaṃ (MN 43) as:

1. Saññā [perception] has just the characteristic of memorizing[sañjānana] (I changed this word for more easier understanding).
2. Its function is to make a sign as a condition for memorizing again that “this is the same [puna sañjānanapaccayanimittakaraṇa],” as carpenters, etc., do in the case of timber, and so on.
3. It is manifested as the action of interpreting by means of the sign as apprehended, like the blind who “see” an elephant (Ud 68–69).
4. Its proximate cause is an objective field in whatever way that appears, like the perception that arises in fawns that see scarecrows as men.

There are more information in the note book of saṅgaha, too:

4. Saññā - Sam + Ö ñā, to know, (Compare Latin cognoscere, to know.)

The meaning of this term widely varies according to the context. To avoid unnecessary confusion, it is best to understand the specific meaning used in the particular connection as a universal mental state.
The chief characteristic of saññā is the cognition of an object by way of a mark as blue etc. It is saññā that enables one to recognize an object that has once been perceived by the mind through the senses. "Its procedure is likened to the carpenter's recognition of certain kinds of wood by the mark he had made on each; to the treasurer's specifying certain articles of jewelry by the ticket on each; to the wild animal's discernment in the scarecrow of the work of man."
Saññā, therefore, means simple sense perception.
"Perception," according to a modern Dictionary of Philosophy, "is the apprehension of ordinary sense-objects, such as trees, houses, chairs, etc., on the occasion of sensory stimulation."
Perception is not used here in the sense employed by early modern philosophers such as Bacon, Descartes, Spinoza, and Leibniz.
As one of the five khandhas (Aggregates) saññā is used in the sense of perception.
Could it be that memory is due to this saññā?
Saññā, viññāna and paññā should be differentiated from one another. Saññā is like the mere perception of a rupee coin by a child. By its whiteness, roundness and size it merely recognizes the coin as a rupee, utterly ignorant of its monetary value. A man, for instance, discerns its value and its utility, but is not aware of its chemical composition. Viññāna is comparable to the ordinary man's knowledge of the rupee. Paññā is like the analytical knowledge of a chemist who knows all its chemical properties in every detail.