The Germany under 20 full-back has played eight matches, four from the start, since arriving on loan from Red Bull Salzburg in January having worked with Oakwell boss Gerhard Struber previously.
Murphy said: “Kilian is a special circumstance. We needed to bolster the backline. He’s a Germany under 20 international. We tried to get a buy option for him but we were told ‘not really’.
"But, because he knows Gerhard, it was a quick transition. We believe Kilian may be able to help us beyond this season so we were willing to go outside our parameters and sign a loan player. I don’t think that is a path we will continue down in full but we will keep our minds open.”
Head coach Struber said: "It is a short-term deal but I have a very good relationship with Kili and maybe we will see what is best for him in his development. The last games show me and Kili that his time here is very good for the development of his personality. I would hope he has maybe a longer time here. We will make a good decision for him and I hope he stays here longer."