The 38-year-old takes charge of his fifth - and potentially final - game of his interim spell at the Oakwell helm against relegation rivals Stoke City tomorrow in a huge 'six-pointer' at the foot of the Championship table.
The Reds hierarchy are understood to have spoken to a number of foreign-based coaches about the vacant position.
Several names have been mentioned including former Ingolstadt head coach Jens Keller, who is understood to have attended the recent home game with Bristol City and been spoken to by the Barnsley board.
Poya Asbaghi, currently managing IFK Göteborg, has been linked with the position, but is no longer an option.
Murray said: "My focus has not changed from Stoke. It is a big game for us and then we go into the international break and I imagine we will come out of the international break with a little bit more clarity on the situation.
"But again, whatever that is, only time will tell."
"My aim when I took over was to make sure the group was in a better place for whenever that decision was made. Whether that is a new manager coming in or an in-house appointment, it does not really matter either way to me.
"My target was to settle the group and I think we have done that and we are in a good place. As far as I am concerned, I have achieved the remit I was challenged with. The club will do whatever they think is best and I will be happy with their decision either way."
Meanwhile, Murray reports no fresh injuries ahead of the game with the Potters.
He said: "Everyone is fantastic and fit and raring to go. There is only Jordan Williams who is not with us at the minute after just starting his rehab on the grass. Apart from that, we are all fit and raring to go.
"We have got a lot of people who are forcing their way to play and we had some good performances from the bench last week and it is a nice problem to have."