Murphy has been out of action since the round-eight game against Adelaide.
"He was out on the track, but we'll just have to see how he pulls up and what the risk is to play him," Blues' coach Brett Ratten told reporters on Tuesday.
"We think he's heading in the right direction, but we'll make a call after today and then we'll see how he goes Thursday.
"He's not a lock-in. Things can change fairly quickly so let's see how he pulls up.
"He's having more physical tests on him, so he's going well."
Both sides are locked on seven wins and sit outside the top eight ahead of Friday night's game at Etihad Stadium.
Midfielder Kade Simpson is expected to miss at least four games with a fractured jaw.
Ratten said tall utility Lachie Henderson (groin) and big forward Jarrad Waite (back) were unlikely to resume this week.
Meanwhile, Ratten says if the Blues have joined the race for Collingwood forward Travis Cloke's signature, he's unaware of it.
Ratten says he expects Cloke to re-sign with the Magpies.
"I'm not 100 per cent sure," Ratten said when asked if the Blues were chasing Cloke, as reported in The Australian newspaper.
"We had list management (meetings) about six weeks ago where we talk about players out of contract. Whether something has happened behind the scenes (I don't know).
"We probably expect Travis to sign with Collingwood very soon but, if there's a good player out there and they want to leave, we'd be interested to talk," Ratten told the afl.com.au website.