US Open champ Simpson could miss British Open
"We haven't made any official decisions because we're going to go to the doctor next week and get an up-to-date projection on the baby," Simpson said after his second round at the US PGA Tour's Travelers Championship on Friday.
"It's not looking likely that I'll be able to go that far."
The Open begins July 19 at Royal Lytham and St. Annes in Lancashire, England.
Simpson said his wife wouldn't be able to travel.
"I'm a guy who loves my family, and we're probably only going to have a couple of more babies," Simpson said earlier this week. "I have the rest of my life to play the British Open."
Simpson admitted his triumph at the US Open at The Olympic Club in San Francisco would make skipping the next major a bit harder, but the memory of seeing the birth of his first son made him determined to be present at the birth of his second child.
"After winning, it's certainly a little harder not to go, because I'd love to go and try to win another major," he said.
"But in the grand scheme of things, in the grand scheme of life, it's a decision that I know that I'll always be happy that I made."