Only once
"You get to play grand slams every year, four grand slams. The Olympics you get to play one time in four years and who knows what will happen in four years for us?
"So I will not risk that and I'll be very honoured and privileged to participate in such an event, an event with the most tradition in sport."
Russian former world number one Maria Sharapova has long cherished competing at the Olympics.
"It's been a dream of mine ever since I was a little girl, so it's been one of my priorities for a very long time," the 20-year-old said, "The Olympics comes around only once every four years and the US Open is there every single year.
"One of the things I'm really looking forward to is the opening ceremony and walking with all the athletes from my country in front of thousands of people."
WTA Tour veteran Davenport was a gold medallist in the women's singles at the 1996 Atlanta Games, two years before she clinched the first of her three grand slam titles.
"It was the first big thing I won and a huge honour," the former Wimbledon, US Open and Australian Open champion told Reuters.
"When I won the US Open in 1998, it seemed to give me more validity as a player. Those two were certainly big turning points in my career and it's hard to compare them.
"I can't wait to go back in early August. It's been on the calendar for my family for a long time. My aspiration is to do my best to win any medal. I really don't care.