Thomas Markle's apparent change of mind comes after Ms Markle contacted him amid widespread speculation over his attendance, celebrity news site TMZ reported.
The US actress's father told the site: "I hate the idea of missing one of the greatest moments in history and walking my daughter down the aisle.
"This is a historic moment. I'd like to be a part of history."
The former lighting director is in hospital where doctors are conducting tests after he complained of serious chest pain after an apparent heart attack last week.
But he appears determined to make his daughter's big day and told TMZ if doctors discharge him from hospital he will travel to England.
Ms Markle and Harry are both deeply concerned for Mr Markle's welfare and are likely to put that priority above the tradition of a father walking his daughter down the aisle.