The representatives for the couple, who haven't yet revealed their little one's name, did not return a request for comment.
Betty, one of the 16 songs from Taylor's eighth album Folklore which she surprise released this Friday, features three names - Betty, Inez and James - the latter two being the names of Reynolds and Lively's three-and-a-half-year old and five-year-old daughters.
This led to fans wondering if the nine-month-old's name had been revealed.
"Betty, I know where it all went wrong... You heard the rumors from Inez / You can't believe a word she says... She said, 'James, get in, let's drive'," Taylor sings.
Folklore is Taylor's follow-up to last year's Lover.