However, a source told the Sunday Times that Harry's closest childhood mentors had been chosen.
Since Diana's death, when Harry was 12, Pettifer has remained close to both of the boys.
READ MORE:
• Megxit: Was Archie's name the first clue in Harry and Meghan's plan?
• Prince Harry and Meghan Markle share adorable new photo of Archie
• Meghan Markle reveals cute nickname for Archie
• Harry and Meghan release new photo of baby Archie
It is believed Meghan was introduced to the former nanny when the pair started dating.
The former nursery school teacher - who once called Harry and brother William "my babies" - was invited to Meghan and Harry's wedding in May 2018.
Mark Dyer is one of baby Archie's godparents. Photo / Getty Images
Harry is godfather to Pettifer's son, Fred.
Archie's other godparent, Dyer, who is a former Welsh Guards officer, acted as a surrogate second older brother to Harry after Diana died.
Harry has remained close with the former Army officer along with his Texan heiress wife, Amanda Kline.
Harry and Meghan have recently quit their official royal duties as they have decided to live in Canada.