Brooklyn, 20, is said to be regarded as the Beeb's chief target, topping a list of 30 celebrity names.
A unidentified source is reported to have told the tabloid: "Brooklyn is the main target for casting chiefs at the moment, because he will appeal to his parents' fans as well as his own.
"He has a young, cool image and they think that will win over new fans. Plus, they would love to get David and Victoria sitting in the front row."
Amelia, meanwhile, is the granddaughter of the Prince Edward, the Duke of Kent, who is the Queen’s cousin.
She should appeal to a young market.
She is 39th in line to the throne in terms of succession - but could she have better chances of lifting the Glitterball trophy?
According to The Sun, senior Strictly crew have been considering bringing a royal on board because they feature so strongly in news outlet headlines.
The insider is said to have continued: "Lady Amelia is both stunning and very young, so she should appeal to a young market too."
Although a royal has not performed on Strictly previously, the 2019 series did include Viscountess Emma Weymouth in the line up.
She and pro partner Aljaž Skorjanec were eliminated from the competition in week 7.
ED! has approached representatives for Strictly, Brooklyn and Lady Amelia for comment.
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