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The OxED has:

Forms: OE–ME assa, ME–17 asse, ME– ass (ME as, ME has, ME a nasse). Pl. ME– asses: OE assan, ME assen, ME asse (south.).(Show Less)

Etymology: Old English assa m. has no exact analogue in the cognate languages. Old English had also ?sol, apparently for ?sel, ?sil, the common Germanic form, = Old Saxon and Old High German esil (modern German esel, Dutch ezel), Gothic asilus, like the Celtic and Slavic names (Old Irish asal, Lithuanian asilas, Old Slavonic osl < *osilu-) evidently < Latin asinus. From the Celtic was the Old Northumbrian asal, assal, assald, the only form in Lindisf. Gospels (occurs 10 times). Of the latter, assa was perhaps a diminutive, formed like the diminutive proper names Ceadda, Ælla, Offa, etc., which at length displaced the earlier ?sol. Assa had also feminine assen, on the type of fyxen, wylfen, ælfen, which did not survive into Middle English, where he-asse, she-asse, occur already in Wyclif. Jack ass, Jenny-ass are modern familiar appellations.
The reputed Old English feminine asse seems to be an error founded on assan folan in which ass is no more feminine than are lion, tiger, in lion's whelp, tiger's cub. The Old Norse asna (feminine), asni masculine appear to be independent late adaptations of Latin asina, asinus, not actually connected with the Old English The Celtic, Germanic, and Slavonic can hardly have been independent adoptions of the Latin: the Slavic was apparently taken through Germanic: was the latter through Celtic? The Ass had no original Aryan name: Latin asinus, Greek ???? (? = ?????), were probably of Semitic origin: compare Hebrew ?th?n, she-ass.
Obs. in polite use.

1. a. The fundament, buttocks, posteriors, or rump of an animal.

c1000 Ælfric Gloss. in Wright 44/2 Nates, ears-lyre.

1377 Langland Piers Plowman B. v. 175 Baleised on þe bare ers [v.r. ars], and no breche bitwene.

?a1398 J. Trevisa tr. Bartholomaeus Anglicus De Proprietatibus Rerum (BL Add. 27944) (1975) I. vii. liv. 407 Emoroydes beþ five veynes þat strecch out attiþ þe ers.

1480 Caxton Chron. Eng. ccxxvi. 233 They lete hange fox tailles..to hele and hyde her arses.

1547 A. Borde Breuiary of Helthe i. f. xviii, The 25. Capytle doth shewe of a mannes ars.

1663 S. Butler Hudibras: First Pt. i. iii. 236 Then mounted both upon their Horses, But with their faces to the Arses.

1704 Swift Full Acct. Battel between Bks. in Tale of Tub 244 Do you think I have nothing else to do..but to Mend and Repair after your Arse? [i.e. behind you, in your rear.]

There appears to be no connection to the modern English ears.

Added in edit (to complete the story), here is what the OxED has for ear:

Forms: OE–ME éare, ME–15 ere, (ME ire, ME ?here, er, erre, ME heer, here, nere, 15 heare) ME–15 eere, yere, ME eire, 15–16 eare, 15– ear. pl. ears; also OE–ME earan, OE earo, earu, ME earen, ME eeren, eren, ( heren, hern, ern).(Show Less)

Etymology: Common Germanic: Old English éare weak neuter = Old Frisian âre, Old Saxon ôre, ôra (Middle Dutch ?re, oore, Dutch oor), Old High German ôra (Middle High German ôre, modern German ohr), Old Norse eyra (Swedish öra, Danish öre), Gothic ausô < Germanic *(?auson-), au?zon-, cognate with Latin auris ( < *ausis), Greek ???, Lithuanian ausis, Old Slavonic ucho, Old Irish ó, of same meaning.(Show Less)

I. The organ of hearing in men and animals. Anatomists distinguish (1) The external ear, consisting of the pinna (the portion which projects outside the head) and the meatus or passage leading thence to (2) the middle ear, or tympanum, a cavity in the substance of the temporal bone, separated from the external meatus by a membrane called the membrana tympani; (3) the internal ear, or labyrinth, which is a complex cavity hollowed out of the bone. In popular language ear is often used for the external ear or the pinna alone.
1. a. The external ear.

OE Riddle 86 3 Wiht..hæfde an eage ond earan twa.

a1400 (?a1325) Cursor Mundi (Vesp.) l. 18836 His hare..Bi his eres skailand sumdele.

c1405 (?c1387–95) Chaucer Canterbury Tales Prol. (Hengwrt) (2003) l. 558 Reede as the bristles of a sowes eerys.

1483 Cath. Angl. 252/2 A Nere, auris.

1556 in J. G. Nichols Chron. Grey Friars (1852) 79 Vij gentylmen of Kent sett on the pyllery..and one of eche of ther erys cut of.

1562 J. Heywood Prov. & Epigr. (1867) 43 Hir eares might well glow, For all the towne talkt of hir.

1661 R. Lovell ???????????????? Isagoge sig. B, The eares..are divided..in the hart, and pilous in the rat.

1746 in W. Thompson Royal Navy-men's Advocate (1757) 34 They would not have let their Ears appear quite so long, had they suspected, etc.

c1750 J. Newton Jrnl. (1836) 64 Some of them said that their ears burned on their heads to hear me speak to such a man.

1842 Tennyson Miller's Daughter in Poems (new ed.) I. 110, I would be the jewel That trembles at her ear.