Billie Jean King says Glasgow hosting the event named after her is a chance to thank Judy, Andy and Jamie Murray for their contribution to tennis.
Dubbed the 'World Cup of women's tennis', the Billie Jean King Cup Finals - formerly the Fed Cup - starts on Tuesday at the Emirates Arena.
The American icon, founder of the Women's Tennis Association in 1973, hopes for an inspirational occasion.
"It's important for Scotland to have this big event," she told BBC Scotland.
"Maybe it will ignite some child, in their heart and mind, to want to play and be a champion. I hope it really inspires some young person in the stands.
"It's an opportunity for us to thank Judy Murray, and Andy and Jamie, for what they've done for tennis. Judy is a positive, great force. Listen to her. Do what she asks because she understands every facet of the sport.
"Andy has been a great ally to women, he believes in equality, he's amazing in that regard. He gets it. Look at how he was raised, he sees how his mother continues to work for our sport."
King is relishing her first trip to Glasgow for the 12-team event comprising four round-robin groups of three, with each winner progressing to the semi-finals.
The 78-year-old - a 12-time Grand Slam champion - had words of encouragement for British number one Emma Raducanu, who was due to lead Great Britain against Kazakhstan and Spain in Group C but has withdrawn because of a wrist injury.
"Emma has already helped put tennis on the map [in the UK] by winning the US Open," said King. "I was very fortunate to be able to give her the trophy.
"Emma is a smart person. I just think we all need to give her space and time. She's had a hard time with injuries.
"I hope she goes to psychotherapy, quite frankly. I think it always helps to have someone to talk to who doesn't have anything to do with her financially but is just on her side."