Beckham, formerly known as Posh Spice, will move to Los Angeles this summer as her soccer-star husband David begins his contract with L.A. Galaxy.
Beckham is reportedly taking the proposal "very seriously" as the media exposure is said to have enhanced Mills' reputation stateside.
A source tells British newspaper The Sun, "We are halfway through the series and it has been massive. A lot is down to Heather.
"We really want Victoria. She's not very popular right now, like Heather wasn't. That's why she'd be perfect.
Beckham's former Spice Girl bandmate Emma Bunton appeared on the original British show, Strictly Come Dancing, last year.
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