The Portuguese now manages Liverpool's bitter rivals Manchester United.
Mourinho has long been seen as an enemy at Merseyside, largely as a result of his fierce rivalry with former Reds manager Rafa Benitez.
But Murphy has revealed that, after Gerard Houllier's departure in 2004, the race to the Liverpool hotseat was between the two men.
Speaking to talkSPORT, the former Liverpool player said: “When Benitez was appointed at Liverpool, it was between him and Mourinho. know that for a fact. Mourinho wanted the Liverpool job massively.
“But Liverpool basically went with Benitez, because he’d just won the Spanish league title and UEFA Cup with Valencia and they thought that was more solid an appointment than someone who had only done it, and that time, in Portugal.
“I know Mourinho was massively disappointed. I’m gutted too, because Benitez came in and didn’t want me. I’m just gutted it wasn’t Mourinho because he might have wanted me to stay!"
Murphy's comments may come as a shock to Liverpool fans after more than a decade of contempt for the current Manchester United manager, but Mourinho certainly was heavily linked to Anfield in the wake of Houllier's sacking.
Liverpool's fortunes, both on and off the pitch, may have been completely different had they appointed Mourinho more than a decade ago.