Royal fans have also touted James Blunt and his wife Sofia Wellesely as potential godparents, with singer-songwriter Blunt sharing a close bond with the Prince after serving in the British military together.
Priyanka Chopra and new husband Nick Jonas are another possibility.
Royal Central suggested the honour could go to at least one foreign royal, Prince Seeiso of Lesotho, a close friend and charity collaborator of the Duke's who was the only royal from overseas to attend the couple's wedding.
It would not be unusual for the Sussexes to elect a foreign royal to stand for Archie.
The Duke of Cambridge has the former King Constantine II of Greece as a godparent, while Prince Charles counts the late King Haakon VII of Norway and Prince George of Greece and Denmark as godparents.
But Kate Middleton and Prince William did not choose a single titled royal, British or otherwise, for their children's godparents.
The future King of England counts Queen Elizabeth's granddaughter Zara Tindall and Jamie Lowther-Pinkerton - former private secretary to the Cambridges and Prince Harry - among the selected seven, Harper's Bazaar reports.
The Sussexes marked Harry's first Father's Day by sharing an adorable new photo of Archie on their official social media account, SussexRoyal.
The stunning black-and-white shot shows little Archie clasping the Duke of Sussex's finger while looking tentatively at the camera.
Baby Archie was introduced to the world for the first time with a photocall at St George's Hall on May 8, two days after his birth.
Harry and Meghan took to Instagram to reveal their baby's name, alongside a photo of the royal couple introducing their newborn to his great-grandparents, Queen Elizabeth and Prince Philip.