The pair came into direct competition on Sunday afternoon as Spurs edged past Ronald Koeman's side courtesy of thrilling 3-2 victory at White Hart Lane.
Barkley and Dembele both started for their respective sides but it was not the first time they had contested a fierce midfield battle.
Barkley played against Dembele as a teenager and told Everton's official Youtube channel - before the Toffees' latest trip to north London - that he rated the 29-year-old highly.
"Mousa Dembele in midfield. I played against him when I was 18 or 19 and I thought it was very tough.
"He's probably the hardest player I've played against. He's a strong player, he gets his foot in well and dictates play."
Dembele is a key member of Mauricio Pochettino's side and has formed a crucial partnership with summer signing Victor Wanyama this season.
The Belgium international is yet to score a Premier League goal this term but often provides the link between defence and attack for the north Londoners, prompting Pochettino to describe him as a "genius".
Meanwhile, Dembele has also made a big impression on his teammates at Spurs, with Dele Alli adamant his fellow midfielder is the best player in Pochettino's squad.