The newlyweds were invited to look round Adelaide Cottage in Windsor to see if they would like to live there, according to the Mail on Sunday.
Until now, the royal couple have lived together in the 1,300 square foot Nottingham Cottage in Kensington Palace.
After Harry and Meghan viewed Adelaide Cottage and took a liking to it, it is understood the Duke and Duchess of Sussex are preparing to make it their second home.
It comes after reports emerged saying the Queen gave the couple York Cottage in Sandringham Estate as a wedding gift in April.
Adelaide Cottage is not privately owned but is part of the Crown Estates, which means that the couple would acquire a long lease, but would not actually own the home.
The grade two listed property is tucked away in the Home Park in Windsor, close to Frogmore House, which was where the international couple celebrated their wedding reception in May.
The park is private and so the Duke and Duchess would be able to enjoy their privacy without fear of intrusion by the public.
The home was first built in the 1800s as retreat for King William IV’s wife Queen Adelaide.
The house was also used by Queen Victoria and Prince Albert as a place for them to relax away from royal life.
In 1945, Group Captain Peter Townsend moved in to the house and most recently the house has been occupied by Simon Rhodes, who is the son of Margaret Rhodes, who was the first cousin of the Queen.
Due to the fact the cottage is a heritage property, the couple will not be able to redecorate or renovate as renters.
The pair were last seen out in public on Saturday at the wedding of Harry’s childhood friend Charlie van Straubenzee to filmmaker Daisy Jenks in Surrey.
The event was on the same day as Meghan’s 37th birthday and Prince Harry was a best man.
Their attendance follows a trying time for Meghan, after her father Thomas Markle gave an explosive interview to the Mail on Sunday.
The former Hollywood lighting director claimed the Royal Family had forced Meghan to freeze him out as he dragged Harry’s later mother Princess Diana into the row.