The 36-year-old, who is currently expecting her fourth child, was said to have looked to the Los Angeles suburb Santa Monica for naming inspiration.
A source told British newspaper The Sun: 'Posh thinks Santa Beckham has a lovely ring to it and wants something unique.
'David prefers something traditional, but will probably go along with what she chooses.'
But the former Spice Girl was quick to deny the rumours.
A spokesman for Victoria, who already has three sons, Cruz, Romeo and Brooklyn, told Vogue: 'This is simply tabloid nonsense.'