Royal aides told the Daily Star that the royal couple have short-listed the traditional name in honour of the Duke of Edinburgh.
William's full name is Prince William Arthur Philip, and his father's name is Charles Philip Arthur George.
A royal insider said that the name Philip is in the frame for a boy and the baby will certainly have it somewhere in his name.
The source said that name is popular with the couple at the moment and could even be the first name as William is very fond of his grandfather.
The aide said William, 30, will make the decision if they have a son.
During a whistle-stop visit to Scotland last week, the couple had kept tight-lipped about their options for names.