Former Liverpool player Alonso is thought to be the favourite to take over at Anfield if Slot loses his job what has been a disappointing season so far.
Alonso was sacked by Real Madrid last week after losing the respect of the dressing room due to a number of disappointing performances under his reign.
Alonso would not fit at Liverpool
Many fans have been crying out for Alonso to replace Slot as they seek to replicate his fantastic form at Bayer Leverkusen, where he led the side to an unbeaten Bundesliga title alongside now Liverpool players Florian Wirtz and Jeremie Frimpong.
However, speaking on the White and Jordan show, Murphy believes that fans will not get what they hope for if Alonso is brought in as his style does not suit the Reds.
"Alonso has this wonderful emotional affinity with the fans because of his time there as a player.
"What I would say is to be careful about that, because although he was a great player, and he's a great lad apparently, and he's a decent coach by all accounts, he's a possession-based coach.
"His Leverkusen were a possession-based team, he grew up with the Spanish way, he was a massive figure in that Spanish team that had years of success by dominating the ball.
"He's not going to be Klopp, so if you want that back, then you're kind of contradicting yourself if you're demanding Alonso, because Alonso won't give you that."
Slot jokes that Alonso has called
Slot joked this week that Alonso had called him and stated that he would take the job in 6 months as the pressure clearly grows on the Dutchman.
"Yes he called me and said: 'What do you think about the team because I am going to take over in six months, can you tell me a little bit more?’"
“Or maybe earlier. Maybe he takes over tomorrow! No, no, no. This is one of the weirdest questions I ever got."