Barkley, who is now 22 years of age and plays as an attacking midfielder, played against Dembele when the Belgium international was at Fulham.
The England international has also named Liverpool and Manchester United legends as players who inspired him when he was growing up.
Liverpool great Steven Gerrard and former United stars Paul Scholes and Rio Ferdinand all made an impression on Barkley.
“It was [Steven] Gerrard, [Paul] Scholes, those types of players,” Barkley told Forever Sports about the England players who inspired him when he was growing up. “And then Rio Ferdinand as well, because I was a centre half when I was a kid.”
“That’s when [Dembele] really kicked on,” said the Everton youngster about facing Dembele, then at Fulham, in his late teenage years.
“The way he manipulated the ball was really good. He was a strong player as well, difficult to play against.”
Barkley scored eight goals and created 55 chances in 38 Premier League appearances for Everton this past season.
The England international attacking midfielder had a pass accuracy of 86% and a shot accuracy of 51%, and won 27 headers, 115 dribbles and 23 tackles.
Dembele scored three goals and created 28 chances in 29 Premier League matches for Tottenham during the 2015-16 campaign.
The former Fulham midfielder had a pass accuracy of 90% and a shot accuracy of 56%, and won 30 headers, 83 dribbles and 84 tackles.