The verse in Vayikra 12:2 says
דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל לֵאמֹר אִשָּׁה כִּי תַזְרִיעַ וְיָלְדָה זָכָר וְטָמְאָה שִׁבְעַת יָמִים כִּימֵי נִדַּת דְּוֹתָהּ תִּטְמָא
If a woman conceives and gives birth to a male, she shall be unclean for seven days; as [in] the days of her menstrual flow, she shall be unclean.
Verse 3 continues
וּבַיּוֹם הַשְּׁמִינִי יִמּוֹל בְּשַׂר עָרְלָתוֹ
And on the eighth day, the flesh of his foreskin shall be circumcised
The flow of the verses, by placing the circumcision as following the end of impurity, seems to be conceptually linking the two, as one conceptually following the other. This is accentuated by the fact that circumcision is seemingly out of place here in the discussion of laws of impurity of a woman who gives birth, and is thrown in as a seeming aside.
Is there some connection between the two?