The Queen recently returned to Windsor Castle, and it is thought she could hold socially distanced talks with Harry if he returns.
Last month Meghan, speaking alongside Harry, urged Americans to get out and vote in the “most important” presidential election of their lifetimes.
In the clip for the 2020 TIME 100 list, the Duke pointed out that he cannot vote in the November 3 showdown between Donald Trump and Democrat Joe Biden.
Senior royals are not allowed to vote in British elections. Traditionally, members of the royal family are expected to be politically neutral but Meghan confirmed she would vote in the US poll.
Palace insiders reportedly told The Sun the Duke "stepped over the line".
A source said: "Staff at Windsor have been told to prepare for the possibility Harry could come back.
"They are told that it could be within weeks but Meghan's name was not mentioned.
"There are all sorts of issues to speak about — not only his political statements but also his visa situation in the US.
"Even though he would have to isolate for two weeks, the estate is large enough for talks in a socially distanced way."
A spokesman for Harry confirmed last month he had paid back the £2.4 million of taxpayers’ money used to renovate Frogmore Cottage by making a contribution to the Sovereign Grant.