The 31-year old Slovenian is out of contract at the KC Stadium at the end of the season but Barmby insists the Tigers are keen for him to remain.
"Whether it's as a manager or a player, you want Robbie Koren to stay," Barmby told the Hull Daily Mail. "We'll definitely be sitting down and hopefully addressing that.
"Robbie has been fantastic since he's been here, he's a great fellow and a great professional. More importantly, he's a match-winner.
"Technically, he's a very clever footballer who causes teams problems when he drifts into space. It's no coincidence that since he's drifted in centrally we've seen the real Robbie Koren."