Redknapp hailed the Dutchman for being 'authentic' as he seeks to fill the shoes left by legendary Liverpool boss Jurgen Klopp, who stepped down at the end of last season.
The Sky Sports pundit believes the former Feyenoord boss has approached the task of succeeding Klopp in an impressive manner.
Liverpool boss Arne Slot has been praised by Jamie Redknapp for his impressive start
‘He is a calm guy, he is not trying to be Jurgen Klopp, he is trying to be his own man and it is going to take time,' Redknapp said.
‘It is going to take a lot of patience.
‘Next week we are going to learn a lot more about him and his team when he has to go to Old Trafford for the first time.
If he can go there and get another three points everything is looking great.
'So far it has been a great start for him. I love how he has played it, it is not fist pumps and trying to be something he is not.
'He is authentic to himself, he is coming across really well, a good football man.
'I am sure the fans are appreciative of what he is doing.
'It seems to have been a calm transition, there is no other way to do it when you are following Jurgen Klopp, you have to be yourself.’
Slot enjoyed a perfect start to life at Anfield as Luis Diaz and Mo Salah scored to secure a 2-0 win over Brentford on Sunday.
Liverpool are one of only four sides to have won their opening two matches at the start of the Premier League season.
The Reds will have a major test next weekend when they face rivals Manchester United at Old Trafford ahead of the first international break of the campaign.