Nicole Johnson is due to give birth to the couple's first child in May. She is with Phelps this week at the Arena Pro Series meet in Orlando, Florida, one of the key tuneup events for the Olympics that begin Aug. 5.
Zika has become an epidemic in Latin America and the Caribbean since last fall. The virus is mainly spread through mosquito bites and has been potentially linked to birth defects.
"We're not worried about it," Phelps told The Associated Press. "I think if you go into any Olympics, there's always something that comes up."
"If she was pregnant, she definitely wouldn't go," Phelps said. "But she's fine about it. She's not missing it. And I wouldn't want the little guy to miss it either. He won't be able to remember it. But he'll have a story to tell."
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Two of the top US female swimmers, Katie Ledecky and Missy Franklin, have no concerns about competing in Rio.
The 18-year-old Ledecky, expected to be one of the biggest American stars, said the US Olympic Committee has done a good job keeping the athletes informed about the potential risks and steps it is taking to ensure their safety.
Franklin, who won four gold medals at the 2012 London Games, expressed a similar sentiment.
"Whenever we go to new countries, USA Swimming and the USOC prepare us for whatever we're going into," the 20-year-old Franklin said. "I know this will be no different." In fact, she's hoping to stay in Rio a few extra days after the Olympics.
"I'm so excited. I've heard so many great things about the culture there," said Franklin, who has never been to South America. "That's my favorite part of traveling, experiencing the culture and the people.