The Manchester United manager's frustrated mood over failed transfer demands has continued through to the season, with the Red Devils losing two of out four Premier League matches.
Meanwhile, Klopp's Liverpool are undefeated and optimism is running high at Anfield. And Murphy believes the two managers are representative of where the two clubs are at the moment.
"At the moment Klopp is everything that Mourinho isn't," Murphy told the Daily Mail.
"Liverpool supporters love his honesty and his enthusiasm. He's ingratiated himself into the club, he's made himself part of it, which is exactly what Mourinho hasn't done.
"Mourinho has been a more successful manager and that's ultimately what counts. But one of the most worrying things about Mourinho is the body language and the lack of fight.
"It's very unlike any other Manchester United team, any Mourinho team to be honest.
"And I don't see how he is going to be able to turn it around that quickly, not unless there's a drastic change in his mentality. I don't see that happening."