The 20-year-olds have since continued their careers at new clubs with Alli now at Tottenham Hotspur and Williams at Fulham in the Championship (second tier) but the prospect of meeting in the Group B encounter is an exciting one for the Welshman.
"That would just be a fairytale story, wouldn't it?" Williams told British media. "Coming up through the same team at 10-years-old and playing against each other in the Euros."
Williams said the recently crowned PFA Young Player of the Year Alli's potential was evident from his academy days, while recalling the competitive spirit that existed between them.
"It was always me and Dele," he said. "It was always who could get one over on the other in training, who could nutmeg someone.
"He can do things with the ball that normal people can't, and the way he thinks on the pitch is unbelievable.
"His work ethic's unbelievable. He's only going to get better. But I could tell from when I first saw him that he was special."
Wales play Slovakia in their opening game on June 11, while England start against Russia a day later.
(Reporting by Nivedita Shankar in Bengaluru; Editing by John O'Brien)
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