He can get impatient all he wants; it doesn't matter. He should check his ego about it at the door before going into a press conference and blabbing to the public about a private matter and hanging one of his players out to dry. And that
has happened - check a few responses on here to see the end result, or go on Twitter if you really want to see the end result of Koeman's actions.
"Contract matters are dealt with internally by the club, it's a club business matter - I won't be making any comment about any player."
That's where Koeman's input in press conferences should begin and end when it comes to contracts.
As an aside, talks only started mid-March. Two months ago. That's not a lot of time. You should be more annoyed at the club than Barkley for leaving it so late.
http://www.telegraph.co.uk/football/2017/03/09/ronald-koeman-will-do-can-keep-ross-barkley-everton/