Prenups are not legally enforceable in the UK, but are increasingly taken into account during divorce cases.
Harry was given £10 million ($19.3m) of the inheritance from his mother, Princess Diana, when he turned 30. He is said to have another £20 million ($38.6m) of assets. Meghan, 36, has amassed an estimated £4 million ($7.7m) fortune from her successful acting career.
Harry would be following the example of his brother, Prince William, who rejected a prenup before tying the knot with Kate Middleton.
Their mother, who also didn't have such an agreement, had to fight hard to win a divorce settlement of £17 million ($32.8m) from Prince Charles in 1996, as well as £400,000 ($772,000) per year.
The Duchess of York fared worse, claiming she received only £15,000 ($28,900) a year from her 1996 settlement with Prince Andrew. However, officials later insisted she had been given a £3 million ($5.7m) lump sum.
A Kensington Palace spokesman declined to comment on the "private matter".