Simon Judges, who is leading the quest for Harold's descendents for English Heritage, says if any exist they are likely to be living in Sweden, the Swedish news agency The Local reports. Harold, like many in England in that era, had close ties by blood and marriage to Scandinavia.
The organization does not plan to put up a rival to Queen Elizabeth II -- a remote descendent of William I.
"This is a 'what if' scenario. We're not into sedition or treason or anything," he said. "There were many challenges to the throne at the time. In a sense, it was more democratic."
In fact, three weeks before Hastings, Harold defeated King Harold Hardrada of Norway, who was also seeking the English throne, at the Battle of Stamford Bridge.
Any descendents of Harold who are identified could become part of an exhibit at a new visitors center on the Hastings battlefield.