But receiving one of the 56 invitations will be difficult, considering commitments to former national and junior national team members. Lieberman will be competing for a tryout spot with college players who are the United States' future.
Many of America's elite women play in Europe or Japan, some earning six-figure salaries. Lieberman makes her living from promotions and endorsements. She would rather stay with her husband in Dallas than play abroad nine months a year. Thus, she trains hard and competes in a men's league in town.
The selection committee probably will not be sympathetic to her situation. A good scoring average in a men's pro-am league simply is not impressive to the standard-bearers of USA Basketball.
"Every point guard in the world will be trying for it this summer," said Susan Blackwood, head of the Women's Games Committee for USA Basketball. "It is going to be tougher."
Moore marveled at the talent assembled last year before the Pan American Games. The players, she said, were rich in international experience.
"No matter how much you work out, no matter how many pick-up games you play in, you can never simulate . . . actual competition," Moore said.
Cline, who has immersed himself in the women's game since his marriage four years ago, hopes his wife will not be overlooked because of prevailing attitudes.
"You can play with all the wonderful females players in the world, but when you start playing college-level male players, it is a whole different ballgame," he said.
The differences might be a disadvantage for a point guard of Lieberman's stature. Recreational leagues tend to emphasize offense in an unstructured atmosphere. Instead of simply whipping her trademark passes, Lieberman must be able to drive past women. That takes the kind of quickness not seen in her era of the mid-to-late '70s.
If the action proves too fast, too strong, Lieberman will have to look elsewhere for a competitive outlet.
For all of those who remember the young redhead whirling around the court, it will be a disappointment. Lieberman's name is painted on the canvas of women's basketball like few others.
She recently published an autobiography, "Lady Magic." Lieberman said she rejected big offers to write a book about her highly publicized three-year relationship with Navratilova. Instead, she wanted to offer an account of her life.
"She has had a lot of experiences outside that three-year window that everybody seems to be so concerned with," Cline said.
Lieberman addressed her relationship with Navratilova, telling the tennis star there was no reason to protect their privacy once the Judy Nelson palimony trial publicly acknowledged their affair last year.
"If I lie about that, I'll lie about other things, and I'm just not going to," she said.
Lieberman and Navratilova remain friends. Lieberman testified at Navratilova's trial, which recently was settled out of court, and Navratilova participated in tennis exhibitions Lieberman promoted.
The interest in their relationship, however, goes beyond personal involvement. "Team Navratilova," with Martina, Lieberman and Renee Richards, became the dominating force of women's tennis from 1981 to '84. Navratilova credits Lieberman with giving her an unshakable resolve to win every match.
Lieberman said something had to give when she first accompanied Navratilova to a practice at the 1981 French Open. Lieberman described the session as a social outing. Navratilova warmed up a little, then hit some baseline shots and a few volleys, then went to the net to talk to Billie Jean King and Betsy Nagelsen. Then she stretched, hit a few more volleys, went to the service line, talked to the other players again and stretched.
That was it.
On the way home, the two stopped at some basketball courts because Navratilova wanted to learn to shoot a layup off her correct foot.
"I'm thinking, 'She barely broke a sweat at practice, and now she is working her tail off to learn how to shoot a layup,' " Lieberman wrote. "I was astonished. How could shooting a layup be more important than preparing to play at Roland Garros Stadium in the French Open? We probably spent more time driving to and from practice than she had practicing."
When Navratilova was eliminated in the quarterfinals by Germany's Sylvia Hanika, Lieberman was in for another shock. Navratilova's tonic for defeat was shopping.
"We made it home . . . after dropping about $15,000," Lieberman said.
As Lieberman's influence increased, Navratilova learned to concentrate on tennis. Lieberman became Navratilova's full-time training partner, and Richards provided court strategy. It was one of the most successful combinations in women's tennis.
By concentrating on Navratilova's career, Lieberman said her basketball skills decreased appreciably. So, when the two parted, she began the arduous climb back.
She has earned some personal victories since then, but the desire to play has not lessened.
"Nancy is almost like Nolan Ryan," said Michael Adams, the Washington Bullets' three-point specialist who played with Lieberman in the USBL.
"She is never going to give it up."
So it would seem. And Sunday she will find out if she gets one more chance.