Bilic's sacking was finally confirmed on Monday morning, more than 36 hours after West Ham slipped into the bottom three of the Premier League.
It is widely expected that David Moyes will be the man who succeeds Bilic at the London Stadium, much to the displeasure of many Hammers supporters, some of whom are calling for a more club-orientated appointment.
Addressing one caller on Talksport earlier today [Monday], however, Murphy urged fans to 'open the box' to an outsider who is first and foremost good at what he does.
"Let me throw you a name out there now. This would be a risk and I know what you might say... The lad at Sheffield United, Chris Wilder, have you seen since he started management what he's done? He's got Sheffield United near the top of the Championship," Murphy said.
"I'm not saying you should go for a Championship manager necessarily at this point, because you might be fighting a relegation battle, what I'm saying is open the box of someone who cares about the club and he knows how it works..."
Sheffield United moved up to second in the Championship after a 4-1 win against Hull City on Saturday, which suggests Wilder could be hard to prise away from Bramall Lane.
The 50-year-old is also a lifelong Blades supporter and recently signed a new deal at Bramall Lane to boot.
Any West Ham move for Wilder would be highly controversial given the two clubs' rivalry in recent years - which was sparked by the 2007 Carlos Tevez affair.