It is a common Ashkenazi minhag to say a Yehi ratzon for the rebuilding of the Temple. The text is based on the words inserted between the two quotes of Yehuda ben Teima in Pirkei Avot 5:10:
:יְהִי רָצוֹן מִלְּפָנֶיךָ ה' אֱלֹהֵינוּ שֶׁתִּבְנֶה עִירְךָ בִּמְהֵרָה בְיָמֵינוּ וְתֵן חֶלְקֵנוּ בְּתוֹרָתֶךָ
To this we add the known phrase:
:וְשָׁם נַעֲבָדְךָ בְּיִרְאָה כִּימֵי עוֹלָם וּכְשָׁנִים קַדְמוֹנִיוֹת
While the last part is from Malakhi 3:4:
:וְעָֽרְבָה֙ לַֽיהוָ֔ה מִנְחַ֥ת יְהוּדָ֖ה וִירֽוּשָׁלִָ֑ם כִּימֵ֣י עוֹלָ֔ם וּכְשָׁנִ֖ים קַדְמֹֽנִיֹּֽת
This very last phrase is said after Elokai netzor, but not after the Korbanot in the morning. Why?
I checked the Machzor Vitry, and the order was quite different back then. The manuscript brings the tamid offering, then the words of Malakhi, then Eizehu mekoman, then the Baraita of Rabbi Yishmael. After this it returns to Leolam yehei adam, and right before Barukh Sheamar only the first part is said.
Emden writes only the first part after the Baraita in this edition from Altona (~1745). However, in this later edition from Warsaw (1881) the second part was added. Heidenheim has all three parts in his machzor from Rödelheim (1800) without the ל prefix. But it's not perfectly clear that it was just inserted later, as this Sulzbach (1701) siddur has all three parts present.