Liverpool have now lost six of their last seven matches in the English top-flight, and suffered defeat in eight of their last 11 games in all competitions, which has led many to believe that their title hopes are now over.
The Reds are in 11th place in the Premier League, trailing league leaders and once title rivals Arsenal by 11 points. Slot is under immense pressure at the moment and many believe he could be sacked if he does not turn the side around.
Speaking on The Gary Neville Podcast, Neville believes it is ridiculous to suggest the Dutchman should be let go and stated that he should be given time to change the situation.
"There's no way that Arne Slot should be in danger or losing his job. I've heard murmurs; you go on social media and all that nonsense, forget that.
"Some Liverpool fans will say, 'Don't talk about my football club like that', but come on, let's have some sense here. This is a really good manager, who's a brilliant frontman for the club as well in the way he handles himself. He's got real class.
"For me, he's having a really bad time. I think he's got to somehow reverse back down the road quite quickly and do something different, intervene and sort out what he thinks might be some really difficult decisions staring him in the face, maybe give the players a little bit of help with the make-up of the teams he is picking.
"For Arne Slot, I think it's a real challenging moment. He's going to come under pressure, people are going to start saying the fatal words of, 'Is he in trouble?' But let's not get too carried away with that. He's just signed £450million worth of players and he's got to try and settle them in.”
Liverpool sit 11th in the table, with 18 points from 12 games, and next face PSV Eindhoven in the Champions League on Wednesday night. Slot must grab a win if he is to stay in the job or face being let go by the club, who are growing impatient.