The Dutchman has led Liverpool to the Premier League title this season at first attempt.
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The Mirror says Fenway Sports Group are preparing a six-year contract offer for Slot after he liftst the Premier League trophy on Sunday at Anfield.
Slot arrived from Feyenoord last summer, signing a three-year deal to 2027.
Asked about spending 10 years at Anfield, Slot said: “I could see it, yes. This club has a history of having managers for a long time and we also saw that with Arsene Wenger and Sir Alex Ferguson.
I think, in general, in football and in life, there is not so much patience. Maybe England is an exception. So I could see myself working here for a long time because it's a great club to work for and I'm really happy over here.”