Defeat at home to Nottingham Forest was a sixth in the Premier League for the title holders, leaving them eleventh on the table.
Keown said, "Whether it's a crisis, I don't know," he said.
"It's certainly a major problem for the manager to go six defeats from seven. Unthinkable. The wheels are coming off now for Arne Slot.
"It was Jurgen Klopp's team and he has tried to come in and make changes, but he has spent £450m on players and they are going backwards."
Former Everton defender Ashley Williams also stated in his pundit's role: "Today's the first time I've thought 'I'm not sure Arne Slot can resolve this situation at Liverpool'.
"Then you start looking at whether they make a change, which seems crazy at the start of the season. They brought (in) good players.
"I thought 'well they've brought three or four of the best players around Europe, they're going to go and steamroll the league again'. They absolutely haven't."