The Merseyside club have the third worst defensive record in the Premier League after seven matches, after Crystal Palace and West Ham United. Liverpool have managed only one win in the last seven matches in all competitions.
A 2-0 defeat to Leicester City in the Carabao Cup saw Liverpool crash out of the competition. However, the former Borussia Dortmund manager boasts an impressive record against the top six clubs in the league at Anfield.
Liverpool's record against the big clubs under Klopp's reign is why the ex-England international centre-back has backed his former club to beat Jose Mourinho's side on Saturday.
"I'm very confident - it's what we [Liverpool] do. Liverpool turn up in the big games. It's going to be an absolute battle but if you look at a lot of our players, they raise their game," Thompson told Sky Sports.
"Dare I say it, but I think there's a good chance of a Liverpool clean sheet. I fancy us as it's here at Anfield and I think it'll be a Liverpool victory."
Thompson also stressed that Mourinho's record against Liverpool while at Chelsea will make the clash "extra-special."
"The relationship between Mourinho and Liverpool makes it extra special - and Jose doesn't mind it," he explained.
"He has always been admired, even before he came to this country. He's created that dislike from the Liverpool fans ever since he was Chelsea boss. It's a bit of a game for Jose.
"He's made it bigger than what it is, including turning Liverpool v Chelsea into a big game which it wasn't in the past. Now he's Manchester United manager it makes it all the more important. The dug-out camera will be brilliant on Saturday."