The 30-year-old American swimmer, who has 18 gold medals, two silvers and two bronze, is eyeing more success in the Brazilian city where the health scare has been a major talking point.
Pregnant women are thought to be at particular risk of the virus due to a link with microcephaly - a birth defect which can cause babies to be born with small heads and under-developed brains.
Phelps' fiancé Nicole Johnson is due to give birth to the couple's first child, a son, in May, with the Games beginning in August.
"We're not worried about it," he said to Associated Press.
"I think if you go into any Olympics, there's always something that comes up."
Phelps added that both mother and child would travel to Brazil, although he admitted Johnson wouldn't attend if she was still pregnant.
Elsewhere, tennis superstar Serena Williams said she would be researching the Zika virus before travelling to Rio and remains cautious.
The 34-year-old American boasts three Olympic doubles gold medals with her sister Venus, won at Sydney 2000, Beijing 2008 and London 2012, as well as the singles title from the British capital.
"I have read a few articles about it but I haven't been following it a great deal," she told Reuters.
"I'm going to have to read a little bit more about it before I can give a proper answer.
"I definitely think it's something that you want to be careful about and we will see what happens.
"God willing, I will be in Rio."
Zika is prevalent in the Americas but has its epicentre in Brazil, with the World Health Organization declaring the situation a "global emergency".
Symptoms - shown by about 20 per cent of people who contract the mosquito carried virus - include fevers, rashes, joint pain, eye redness and conjunctivitis.
Advice for athletes includes wearing long sleeve clothing, applying insect repellent, the use of mosquito nets and sleeping in air conditioned rooms, while Brazil has desperately been trying to curtail the virus in the run-up to Rio.
The Brazilian Ambassador to Kenya, Mercela Nicodemos, has attempted to reassure people in the African country after its National Olympic Committee President Kipchoge Keino suggested the country, an athletics powerhouse, could withdraw if Zika reached "epidemic" levels.
"A huge effort has been put in to combat the virus to safeguard the well being of its citizens and visitors," said Nicodemos.
"We are confident by August, there will be no risk at all."
It is hoped that cooler weather during Games time will mean that the mosquitoes carrying Zika are less prevalent.