Carling Bassett-Seguso was a world No. 8 almost 30 years ago. Currently 13th, Bouchard is assured of equalling that when the next rankings are released Monday.
The 20-year-old from Westmount, Que., became the first Canadian woman to reach Wimbledon's semifinals with a 6-3, 6-4 win over ninth-seeded Angelique Kerber of Germany on Wednesday.
"I'm telling you she's going to number one," Bassett-Seguso told The Canadian Press. "I watched her play. I don't watch too much women's tennis to be honest with you. I watched that match and I was just blown away.
"She just takes the ball so aggressively. Her composure, I can't even believe she's 20. Her shot selection, her timing is impeccable. She really takes the ball early. If you look at her statistics, she hits more winners than errors."
A victory over third-seeded Simona Halep of Romania in Thursday's semifinal can push Bouchard's ranking higher than eighth and set a new pinnacle in Canadian women's tennis.
Bassett-Seguso intends to be watching from her home in Bradenton, Fla., as Bouchard attempts to make more Canadian tennis history.
"It gives me great interest to watch now," the 46-year-old said. "She has such great potential.
"I love Wimbledon. I look at it and say 'they hit the ball way harder than I did.' It's a totally different game now. What's exciting is she can hit a lot of other shots too. I like to see the creativity too."
Bouchard also reached the semifinals of this year's French Open and Australian Open. Canada's Federation Cup captain Sylvain Bruneau agrees with the Bassett-Seguso's assessment of Bouchard's potential.
"Can she be No. 1 one day? I wouldn't dare to put any limits on Eugenie," he said. "With three semifinals at 20 years old and the type of tennis she plays, I don't think there is a limit.
"I think she can aim for big things in tennis. No. 1 in the world is something that is very possible. Right now, she's playing great tennis."
These are heady days in Canadian tennis. Milos Raonic of Thornhill, Ont., also earned his first Grand Slam semifinal berth Wednesday with a 6-7, 6-2, 6-4, 7-6 (4) win over Australia's Nick Kyrgios.
Bassett-Seguso, who blazed her own tennis trail in the 1980s, is enjoying it from afar.
"For me, it's great," she said. "There's a big interest and I think it's going to be such a great asset to Canadian tennis itself, on the men's side too."
Toronto's Bassett-Seguso turned pro at 15 in 1983 when there were no age minimums to play on tour. She reached No. 8 in the world two years later.
She was a semifinalist at the U.S. Open in 1984 when she lost to Chris Evert. She also reached the quarter-finals of the Australian and French Opens during her career.
She married U.S. tennis player Robert Seguso in 1987. The couple once ran a tennis academy in Florida, but are no longer involved in the sport. They have five children ranging in age from two to 26.
The blonde, photogenic Bassett-Seguso became a Canadian celebrity with the nickname "Darling Carling." The teenager worked for the Ford Modelling Agency. She acted in the teen movie "Spring Fever", as well as a television episode of "The Littlest Hobo."
The success came with pressure, however. Bassett-Seguso struggled with an eating disorder during her career. She lost some of her passion for the game after the death of her father John in 1986 from cancer, although she continued to play on tour until 1990.
Bouchard, also tall and blonde, is likewise attracting her share of attention, and endorsements, as her career soars. She has a significant following on social media and her fan club is "Genie's Army."
But joining the world's top 10 players requires unwavering commitment to the sport, Bassett-Seguso said. Tennis is a world sport with 145 countries as members of the International Tennis Federation.
"It's hard. I'm not going to lie. It's really hard," Bassett-Seguso said. "I don't think anything is too hard if you want something bad enough and you have a plan and you have the right people around you and you know what has to go into it.
"You're going to fall (in the rankings) at times and that's where you have to constantly believe in yourself and take baby steps. You have to stay focused. Tennis has to be your whole life. It has to be."
Canadian Press sports reporter Bill Beacon contributed to this story.
Follow @DLSpencer10 on Twitter.
Also on HuffPost