England face Argentina later on Wednesday and should they win to meet Spain, they would be in their first World Cup final since 1966. The match in New Jersey kicks off at 21:00 CET.
Traditionally, the last putt at The Open drops at around 19:30 CET but should it go to a playoff, it could overlap with the World Cup, leaving fans with a dilemma.
Addressing the scenario on Wednesday, R&A Chief Executive Mark Darbon said no decision had been made.
"I'm an England football fan, so it would be a great problem to have. But I guess also, because I'm an England football fan, we should also wait to see how the semi-final goes before we get too far ahead," he told reporters on Wednesday.
"We think that even if we go to a three-hole playoff, we've got time to complete the championship. So at this stage, no plans to alter anything, but we'll maintain that under review and finalise our position after the semi-final."
The 154th Open begins on Thursday on the coastal links just north of Liverpool where the hot and dry weather is expected to last for most of the championship.
"It's going to play fast and firm and offer a true links test to our incredible field," Darbon said.
A record attendance of 300,000 is expected throughout the major, and while British Open crowds are generally regarded as respectful, a new fans' code of conduct has been introduced to ensure that standards are maintained.
Several high-profile golf events such as the last Ryder Cup and the US Open have been tarnished by boisterous and rowdy fan behaviour often fuelled by excessive alcohol.
The R&A's fan code of conduct, called 'The Open Commitment', has five cornerstones - Respect the Players, Respect the Links, Respect Each Other, Be Aware, Enjoy Responsibly.
"We thought by codifying some of what we expect, it will help and support this championship moving forward," Darbon said.