It is unclear whether Meghan Markle’s father Thomas will walk her down the aisle on Saturday as planned.
Mr Markle is reported to have told journalists at his home in Mexico that he had decided not to attend.
Kensington Palace has issued a statement asking for “understanding” to be extended to Mr Markle in this “difficult situation”.
It follows Mail on Sunday reports that Ms Markle’s father had staged pictures for a paparazzi photographer.
The widely circulated photographs showed him being measured for a wedding suit and looking at newspaper stories about his daughter.
He is reported to have said that he didn’t want to cause his daughter embarrassment by attending the wedding.
A Kensington Palace spokesman said: “This is a deeply personal moment for Ms Markle in the days before her wedding.
“She and Prince Harry ask again for understanding and respect to be extended to Mr Markle in this difficult situation.”
Mr Markle had been due to meet Prince Harry for the first time this week, as well as the Queen and the Duke of Edinburgh, before walking his daughter down the aisle at St George’s Chapel in Windsor Castle.