Slot has also emulated legendary Liverpool boss Bill Shankly by winning his first three European matches as manager.
Liverpool’s impressive start to the season includes wins against Manchester United, AC Milan and Chelsea.
There are some big tests on the horizon. As well as Arsenal, they have matches against German champions Bayer Leverkusen, Aston Villa, Real Madrid and Manchester City between now and 1 December.
“This is a team on a brilliant run with some players playing well, but it’s clear more improvements will come,” said Nevin.
“If you are having this sort of run and nowhere near peaking yet, that’s real good news.
“Arne Slot’s aware of it. There’s more to come from this team, but you wouldn’t think so from the results.”
After the Leipzig game, Slot said his players must be proud after achieving the “almost impossible” feat of setting new club records.
Like Klopp, Slot is aware he will be judged on the number of trophies he brings to Anfield – not records.
“Records are nice, but other things are nicer than records and you know what I mean by that – trophies,” Slot said.