Slot has enjoyed an impressive start to life at Liverpool having succeeded Jurgen Klopp, with the Reds one point clear at the top of the table after seven matches.
Liverpool will face a major test on Sunday when they host Chelsea at Anfield.
The visitors have shown improvement under Maresca following a turbulent couple of years, with the Italian leading his side to fourth in the early season table.
Liverpool legend Carragher, writing in his Telegraph column, believes Sunday's match could be the first in a new rivalry between the two teams.
Arne Slot has led Liverpool to the top of the Premier League ahead of their match with Chelsea
Carragher suggested respective managers have the potential to push their teams into the frame for the title, disrupting the battles between Man City and Arsenal in recent seasons.
He cited the clashes Liverpool and Chelsea under previous managers, as well as battles in the transfer market and the Reds victory in last year's Carabao Cup final as a sign animosity between the teams could return.
'If the hostility gets back to what it was, it will be good news for the clubs and the Premier League,' Carragher wrote.
'There is much work to be done by Maresca and Slot to get that far, but I have a sneaking feeling that Sunday is the first of many duels between coaches who, in time, will be going head-to-head for the biggest prizes.'