Instead, Mourinho was snapped up by Chelsea and went on to win three Premier League titles, three League Cups and the FA Cup across five years in two spells.
Benitez, who now manages Newcastle United in the Championship, guided Liverpool to Champions League success, as well as an FA Cup final win and the Super Cup in a six-year stint.
Murphy has claimed that Mourinho was keen to take the Anfield hotseat, and the former midfielder wishes he had given that he himself was sold to Charlton Athletic during Benitez's first season at the club.
"When Benitez was appointed at Liverpool, it was between him and Mourinho - I know that for a fact," Murphy told talkSPORT. "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!"
Mourinho has been under the spotlight recently at United following three consecutive defeats last week, but his team bounced back in the EFL Cup on Wednesday night when they earned a 3-1 win over Northampton Town in the third round.