This morning I listened to a compilation album of the Andrews Sisters, and I think I found some allusions in "Where Have We Met Before?"
The second verse begins with the lines: "It might have been way back in Nagasaki / Where women wicky wacky 'round your door." I think this is a reference to the song "Nagasaki." Apparently this is a jazz standard, but I have only Django Reinhardt's version, which has the lines "Back in Nagasaki where the fellas chew tobaccy / And the women wicky wacky woo."
The third verse of "Where Have We Met Before?" begins with "It might have been in Paris in the springtime," which I think is a reference to "April in Paris." It's not as direct as the allusion to "Nagasaki," but April is in spring, so the temporal elements do match.
I lookt up the dates for these songs, and I think the chronology allows for the allusions. The dates I found say that "Nagasaki" is from 1928; "April in Paris" is from 1932; and the Andrews Sisters' "Where Have We Met Before?" is from 1938.
I can't fully articulate it, but there's something fitting about referencing other songs in a song that asks, "Where have we met before?"