Konta's quarter-final against Romanian second seed Halep, who will become the world number one if she progresses, is the third match on Centre Court.
Halep did her best to avoid the topic when cross-examined after her confident 7-6, 6-2 win over double Grand Slam champion Victoria Azarenka.
Halep reached the semifinals at the All England Club in 2014 and played in the quarterfinals previous year.
Halep was favourite for the French Open and found herself in the final, but she eventually fell in three hard sets to the unseeded Jelena Ostapenko. "I stayed mentally quite tough, tried just to knuckle down on every single point I could".
"I think physically I certainly could have played a fifth set if it was required".
Second seed Halep is the sole player left in the competition ranked higher than the 26-year-old after defeats for world No1 Angelique Kerber, Ukraine's Elina Svitolina and Caroline Wozniacki of Denmark.
She would thus become the first Romanian to reach this position.
So it went to a tie-break but Konta, to her credit, did not allow her frustration to deter her.
Garcia lost the first set to the Brit in a tie-break but fought back to take the second 6-4.
In 2014, she switched her training base to Gijon in Spain working with her Spanish coaches Esteban Carril and Jose-Manuel Garcia.
She counts her best tennis memory so far as representing Great Britain at the 2016 Olympics.
However, bad blood aside, Konta remained much more philosophical in her answer.
The second Monday of Wimbledon promises a thrilling day of tennis for fans flocking to SW19, with the last 16 men and women in the singles draw all scheduled to play.
This was Williams' first match since police in Florida rescinded their original conclusion that she was at fault in a two-car crash last month.
Clijsters, who claimed three US Open titles and also won the Australian Open during her illustrious career, added: "I think a lot of them believe they can do it, but really don't know how. or the belief causes pressure and they really don't know how to deal with it when the time is right to do that".
Beaten in the 2015 final by Serena, Spain's Garbine Muguruza admits she and many of her title rivals know they have a golden opportunity to lift the Venus Rosewater Dish while the 23-time major victor is away.
The Frenchwoman Andy Murray predicted as a potential number 1 in 2011, after missing four chances broke to 2-1 as Konta overhit a forehand before slamming a return into the net.
However, her tennis career nearly ended before it began after she lost her financial support when the team had its funding cut.