The new father is thought to want Alves to design her own bespoke diamond engagement ring to her own taste, whether she prefers platinum diamond rings or gold diamond rings.
"Camila was absolutely overjoyed - a baby and a marriage proposal on the same day," a source told the publication.
The new arrival reportedly helped the star realise that his top priority was his family, although a date has not been set for the ceremony.
Following Levi's birth, McConaughey told OK! Magazine that he played recordings of "this native Brazilian music" during his partner's 14-hour labour.