The Duke and Duchess shocked the world in January when they announced they were stepping down from senior royal duties. They have since relocated to Canada with their son Archie Mountbatten-Windsor.
According to the Sunday Times Meghan and Harry have accepted an invitation from the Queen to stay at Balmoral over the summer.
Each year the Queen spends part of the summer at Balmoral, her country estate in Scotland.
Here she is typically visited by other members of the royal family, who are often invited to stay for a period.
Last year Harry and Meghan are believed to have rejected an invitation to stay at Balmoral.
The decision, which reportedly left the Queen “disappointed”, was apparently made as the couple felt their son was too young to make the trip.
Meghan and Harry recently returned to Canada after a brief visit to the UK, which saw them undertake their final engagements as senior royals.
The couple attended the Commonwealth Day service in Westminster Abbey, along with the Queen, Prince Charles and the Duke and Duchess of Cambridge.
Meghan also visited Robert Clack School in Dagenham to talk about international women’s day.
Meghan and Aker also hugged during the visit.
Speaking to the Sun on Sunday Aker said: “There were rumours a big name was visiting but nobody expected Meghan.
“It was incredible. She was lovely and down-to-earth.
“She didn’t seem to mind me kissing her and saying she was beautiful.
“She laughed, along with the whole school.”
After negotiations with other senior royals Meghan and Harry agreed to drop their ‘Sussex Royal’ brand.
They have also pledged to repay the public money spent refurbishing Frogmore Cottage, near Windsor, where the couple lived before moving to Canada.
Harry and Meghan’s UK visit also saw them attend the Mountbatten Festival of Music at London’s Royal Albert Hall.
The event brought together world-class musicians, composers and conductors of the Massed Bands of Her Majesty’s Royal Marines.
Harry attended in his role as Captain General Royal Marines – a position he will relinquish when the Sussexes step down as senior royals at the end of the month.