They say they have been emailed about the coronation, on 6 May, but will not confirm whether they plan to attend.
It is understood that some prospective guests are being asked to save the date ahead of official invitations that will be sent later.
Buckingham Palace has declined to comment on invitations.
There has been speculation about whether the US-based couple would be invited, and whether they would attend the coronation of King Charles and Camilla, the Queen Consort.
A statement from Prince Harry and Meghan said they had been contacted about the coronation.
"I can confirm the Duke has recently received email correspondence from His Majesty's office regarding the coronation," a spokesperson for the couple said.
"An immediate decision on whether the Duke and Duchess will attend will not be disclosed by us at this time."
Westminster Abbey, where the coronation will take place, has capacity for about 2,200 guests. Many public figures, politicians and international dignitaries are expected to attend, as well as the King's family and friends.
Formal printed invitations are expected to be sent closer to the time, but it is believed that some groups of guests are being approached in advance, advising them to save the date.
The focus on whether Prince Harry and Meghan will come to the coronation follows revelations in his memoir about tensions with his family.
This included an account of an altercation with his brother Prince William, who as Prince of Wales is likely to have a role in the coronation ceremony.
In a previous interview about his memoir, Prince Harry had declined to say whether he would attend his father's coronation, saying: "The door is always open. The ball is in their court."
If Prince Harry does return for the coronation, it is not known what part he might play, as he is no longer a "working royal".
During the Queen's Platinum Jubilee, Prince Harry and Meghan were not part of the appearances on the Buckingham Palace balcony. These traditional appearances for the crowds will also be part of the coronation celebrations.
In an online interview on Saturday, Prince Harry said he had always "felt slightly different" to other members of his family - and that his late mother, Diana, had felt the same.
It also emerged last week that Prince Harry and Meghan had been asked to vacate Frogmore Cottage, the couple's UK base in Windsor.
-- Courtesy of BBC News