Hibs reported “significant progress” has been made in their managerial search, with Brown this week confirming he had been interviewed for the vacancy after 23 years as assistant to Jim Jefferies, including two spells at Hearts.
But Murray believes Brown’s previous affiliation to Hibs’ Edinburgh rivals should be no barrier to his appointment on a permanent basis, should the Easter Road board choose in his favour.
Bohemians’ Pat Fenlon and Michael O’Neill, of Shamrock Rovers, are also reportedly in consideration for the position.
Murray said: “Billy’s been here a couple of months now, so he knows how the players work and how the place is run. The fact that Billy’s been at Hearts before is no different to being anywhere else.
“We all understand that he’s worked with Jim for so long and it’s maybe time he wants a shot of it on his own.
“There’s no better place for Billy than Hibs. He’s worked for so long and in the SPL as well, which is a huge benefit for us.
“The board of directors and chairman will know Billy’s strengths. If the board of directors feel he deserves it, he deserves it.
“They’re the ones making the decisions on who manages us.
“We’re just trying to concentrate on ourselves because we know as a group of players any manager can come in here and train us for five days a week, six days a week, and if we don’t go out and do it on a Saturday we won’t be here very long.”
Murray and the players are aware of their role in Calderwood’s departure after 12 months in the job and 12 wins in 49 matches.
He added: “I think we’re all sensible enough to realise that we got the manager the sack, no-one else.
“He gave us everything. We didn’t give him it back, basically. That wasn’t from not trying. There were certain players that let him down.
“No doubt, I’d like to go back and play some games differently. I’m sure we all would. If the players think it isn’t their fault then there’s something wrong – the buck stops with us. We let ourselves down, first and foremost, we let the fans down and we let our previous manager down.
“We’re all playing for our futures. There will be players getting shipped out, that’s a certainty.”
Although Hibs enter this weekend’s fixtures a point off the foot of the table in ninth place, Murray insists it is too soon to talk of a relegation battle and believes his side may even be capable of finishing ahead of the pack currently chasing Rangers, Celtic and Motherwell.
He said: “The league is very tight. I wouldn’t like to say who’s going down at the moment. We feel we’re far away from being the worst team in the league and we feel we can get up to fourth this season.
“Motherwell are doing well and I’ve been impressed by them but we see no reason why we can’t get up there.”
Brown could be without Leigh Griffiths as he tries to secure a victory which might help add weight to his prospects of landing the job permanently. On-loan Wolves striker Griffiths has had a stomach bug this week, but is the only concern. Murray, Callum Booth, Matt Thornhill, Michael Hart and Sean Welsh are all available following injuries.
Kilmarnock look set to be without David Silva, who picked up a knock during a practice match earlier in the week and is likely to miss a trip to Easter Road that defender Garry Hay expects will be even tougher than usual.
“Billy will be looking for a positive response from the players on Saturday and that’s what we are expecting,” said Hay.
“Far from being down in the dumps, they will be right up for the game and we have to be as well.”