The Dutchman is keen to see the Everton star flourish after a disappointing summer.
Everton manager Ronaldo Koeman
Barkley endured a difficult campaign last season, posting his best numbers in terms of goals and assists but struggling for consistency under Roberto Martinez.
The second half of the season was something of a disaster, with him failing to score in the Premier League after February 6th, his last strike coming against Bournemouth in the FA Cup on February 20th.
Everton's Ross Barkley scores their second goal
It ultimately cost him in the summer, as former England manager Roy Hodgson took him to Euro 2016 but failed to hand him a single minute in their dismal tournament.
Nonetheless it is a fresh start for him at Goodison Park now under his new manager, and he says he has urged the midfielder to show his best form.
“He is one of the key players who is performing in an important position for the team,” he told the Daily Mail.
“But he also need to show more responsibility in terms of the defending part of the team. That is one of the aspects in football where he can improve. I have told him how I see Ross Barkley and where he needs to improve.”
Ross Barkley celebrates scoring the third goal for Everton
It now remains to be seen if Barkley can shine under Ronald Koeman’s guidance this season.
He certainly has a point to prove, with Roy Hodgson not the only one to have written him off this summer.
What will be interesting to see is whether he can deal with that added defensive responsibility Koeman wants him to taken on, with that a very different approach to the one Martinez took.
Everton manager Ronald Koeman