In context, the word adam - אדם – in this verse means person. But the Midrash expounds and takes the word to mean Adam, as in primordial man. Here is that midrash:
ויקרא רבה 2:7
אָמַר רַבִּי בֶּרֶכְיָה אָמַר לוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא לְאָדָם זֶה, אָדָם, יְהֵא קָרְבָּנְךָ דּוֹמֶה לְקָרְבָּנוֹ שֶׁל אָדָם הָרִאשׁוֹן שֶׁהָיָה הַכֹּל בִּרְשׁוּתוֹ וְלֹא הִקְרִיב מִן הַגְּזֵלוֹת וּמִן הַחֲמָסִים, אַף אַתָּה לֹא תַקְרִיב מִן הַגְּזֵלוֹת וְלֹא מִן הַחֲמָסִים, וְאִם עָשִׂיתָ כֵן (תהלים סט, לב): וְתִיטַב לַה' מִשּׁוֹר פָּר.
[“When a man [adam] among you sacrifices.”] Rabbi Berekhya said: The Holy One blessed be He said to this man: ‘Man, let your offering be similar to the offering of Adam the first man; everything was in his domain and he did not sacrifice from that which was stolen or extorted. You, too, do not sacrifice from that which was stolen or extorted. If you do so: “It will please the Lord more than a bull”’ (Psalms 69:32).
Rashi liked this midrash, so he cited it in his commentary on the Torah:
רשי, שׁם
אדם. לָמָּה נֶאֱמַר? מָה אָדָם הָרִאשׁוֹן לֹא הִקְרִיב מִן הַגָּזֵל — שֶׁהַכֹּל הָיָה שֶׁלּוֹ — אַף אַתֶּם לֹא תַּקְרִיבוּ מִן הַגָּזֵל (ויקרא רבה)
אדם — Why is this term for “man” employed here? Since אדם also means Adam, its use suggests the following comparison: what was the characteristic of the first man (אדם הראשון)? He did not offer sacrifice of anything acquired by way of robbery, since everything was his! So you, too, shall not offer anything acquired by way of robbery (Leviticus Rabbah 2:7).
The Keli Yakar, a commentary written by Shlomo Ephraim ben Aaron Luntschitz (1550-1619) liked another midrash, found in the Talmud (Shabbat 28b). So he connected the two:
כלי יקר שם
וזה"ש (שבת כח:) שור שהקריב אדה"ר קרן אחת היה לו במצחו לכך נזדמן לו שור בעל קרן אחת כי היה דומה אל האדם שהיה קרן א' ר"ל שהיה יחידי בעולם ולא גזל משום אדם, ולא נתעורר משום אדם, כ"א מעצמו דהיינו מכם ע"כ עלה קרבנו לרצון נמצא שקרבן לה' הפסיק הענין. ואח"כ אמר מן הבהמה וגו' להוציא זרע פשתן אלא יעשה כהבל שהביא מבכורות צאנו. ומה שאמר תקריבו קרבנכם היינו מחלביהן החלק המובחר שאדם בוחר לעצמו הנקרא קרבנכם אותו תקריב לגבוה ונקט קרבנכם לשון רבים כפירש"י לומר שב' מקריבין בהמה
This is what is referred to [in the Talmud Shabbat 28b] “the ox that Adam sacrificed had but a single horn on its forehead,” mirroring Adam who was a single person in the world…
And here is the talmudic discussion as found in Shabbat:
תלמוד בבלי שבת כח, ב
מִדְּקָאָמַר קֶרֶן אַחַת הָיְתָה לוֹ בְּמִצְחוֹ, שְׁמַע מִינַּהּ טָהוֹר הָיָה, דְּאָמַר רַב יְהוּדָה: שׁוֹר שֶׁהִקְרִיב אָדָם הָרִאשׁוֹן קֶרֶן אַחַת הָיְתָה לוֹ בְּמִצְחוֹ, שֶׁנֶּאֱמַר: ״וְתִיטַב לַה׳ מִשּׁוֹר פָּר מַקְרִין מַפְרִיס״. ״מַקְרִין״ תַּרְתֵּי מַשְׁמַע! אָמַר רַב נַחְמָן בַּר יִצְחָק — ״מַקְרָן״ כְּתִיב
… as Rav Yehuda said in a similar vein: The ox that Adam, the first man, sacrificed as a thanks-offering for his life being spared, had a single horn on its forehead, as it is stated: “And it shall please the Lord better than a horned [makrin] and hooved ox” (Psalms 69:32). The word makrin means one with a horn. The Gemara asks: On the contrary, makrin indicates that it has two horns. Rav Naḥman bar Yitzḥak said: Despite the fact that it is vocalized in the plural, it is written mikeren without the letter yod to indicate that it had only a single horn….
Rabbi Yehudah does not suggest just what animal this might have been, but that doesn’t stop us from trying to do so.
How about a unicorn? To understand this suggestion we need a little more background.
THE RE'EM IN THE BIBLE
The word ראם, re'em appears several times in the Hebrew Bible. Here, for example, is a verse from Deuteronomy (33:17) which describes the offspring of Joseph.
דברים לג: יז
בְּכ֨וֹר שׁוֹר֜וֹ הָדָ֣ר ל֗וֹ וְקַרְנֵ֤י רְאֵם֙ קַרְנָ֔יו בָּהֶ֗ם עַמִּ֛ים יְנַגַּ֥ח יַחְדָּ֖ו אַפְסֵי־אָ֑רֶץ וְהֵם֙ רִבְב֣וֹת אֶפְרַ֔יִם וְהֵ֖ם אַלְפֵ֥י מְנַשֶּֽׁה׃
Like a firstling bull in his majesty, He has horns like the horns of the re'em; With them he gores the peoples, The ends of the earth one and all. These are the myriads of Ephraim, Those are the thousands of Manasseh.
The re'em is specifically identified by the great translator of the Bible Oneklos (~35-120 CE) as one of the species singled out in the Torah as being kosher:
דברים יד: ד–ה
זֹ֥את הַבְּהֵמָ֖ה אֲשֶׁ֣ר תֹּאכֵ֑לוּ שׁ֕וֹר שֵׂ֥ה כְשָׂבִ֖ים וְשֵׂ֥ה עִזִּֽים׃ אַיָּ֥ל וּצְבִ֖י וְיַחְמ֑וּר וְאַקּ֥וֹ וְדִישֹׁ֖ן וּתְא֥וֹ וָזָֽמֶר׃
These are the animals that you may eat; the deer, the gazelle, the roebuck, the wild goat, the dishon, the antelope, the mountain sheep.
Onkelos translates that word דִישֹׁ֖ן into Aramaic as רֵימָא - the re'em. And then there is this passage from the Book of Job (39:9-12):
איוב לט:ט–יב
הֲיֹ֣אבֶה רֵּ֣ים עָבְדֶ֑ךָ אִם־יָ֝לִ֗ין עַל־אֲבוּסֶֽךָ׃ הֲֽתִקְשָׁר־רֵ֭ים בְּתֶ֣לֶם עֲבֹת֑וֹ אִם־יְשַׂדֵּ֖ד עֲמָקִ֣ים אַחֲרֶֽיךָ׃
Most English versions of this passage translate the word re'em as "wild ox"and so read:
Would the wild ox agree to serve you? Would he spend the night at your crib? Can you hold the wild ox by ropes to the furrow? Would he plow up the valleys behind you?
But not the King James Bible. It goes in an entirely different direction:
Will the unicorn be willing to serve thee, or abide by thy crib? Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee?
So according to the King James Bible, the re'em is a unicorn. Why on earth would the translators have chosen, of all creatures, the mythical unicorn as the re'em?