Salah, 32, is out of contract at Anfield at the end of the season and said last week he was "disappointed" by the club's failure to offer him a new one.
The Egyptian again highlighted his worth at Newcastle, creating Liverpool's opener for Curtis Jones and then scoring two excellent finishes before Fabian Schar's late, late equaliser.
Slot told Amazon Prime: "Every time we need Mo Salah he scores a goal.
Robbie Fowler scored 128 times in the Premier League for Liverpool and was in no doubt about how the club should handle Salah's future.
Speaking on Amazon Prime, Fowler said: "Salah's stats and data are incredible. We talked about him getting that new contract and his agent should be there first thing in the morning to get him to sign that contract.
"He is that player who can change a game. He has moments and he is exceptional in those moments. He is a match winner."
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