Murphy is due to play for Motherwell against Celtic on Wednesday but that will almost certainly be his last game for the club.
Well manager Stuart McCall said: "I believe he is in discussions with a club.
"He will certainly be playing against Celtic and depending on how discussions go, it looks more than likely that he will move.
"I believe Sheffield United are the club he is possibly speaking to.
"Who knows, the way he has been playing in the last few months there could be other offers."