"Victoria feels as though she has a proper shot at becoming the godparent," a source close to the Beckham's told UK's heat magazine.
"Vic has been spending quite a bit of time with Meghan lately and heard rumours that she may be asked. She absolutely loves having a connection to royalty and this would be the ultimate honour."
The insider added: "She's been doing everything she can for Meghan by sending her lots of free clothes, and inundating her with interior design advice for Frogmore Cottage. She doesn't want to crowd Meghan, but at the same time she wants her to know that she's there for her 24/7 and would be for the baby, too."
However, Victoria is believed to be worried husband David could ruin it all.
"Victoria is terrified of him making some public mistake in the run-up to the birth," the source adds.
"She's told him he needs to step up and act more of a dutiful husband in the public eye to prove they're the perfect choice for Meghan and Harry. She's really piling on the pressure - she is exhausting herself, but she feels it will be worth it if they can pull this off."
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