The Hungary captain says there are differences between Slot and predecessor Jurgen Klopp.
He told liverpoolfc.com: "It's a little bit different – the style of playing, how we play, how we are with the ball and also against the ball.
"Everybody's in from the training staff, we are getting to know them. I think everybody is happy with it and we are looking forward.
"It's quite intense but we have a lot of things to do and we need to be intense in the season as well."
Szoboszlai added, "It can always be better. Last year we finished third and won the Carabao Cup.
"This year, Champions League is back again – where we belong – and we want to show ourselves there as well. We are going for the Premier League again.
"I'm feeling very good, getting ready for the new season. Big games ahead of us, big season, new challenges, so I think everybody is getting ready."