The Reds have looked very shaky at the back in recent weeks.
And Thompson’s prediction looks even bolder given that Liverpool have to failed to stop an opposition team scoring since their 4-0 win against Arsenal on August 27.
However, Thompson - who played 340 games for the Reds - says his former club always rise to big occasions.
"I'm very confident - it's what we [Liverpool] do," he told Sky Sports.
"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.
"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 is right in his assertion that Liverpool do well against the Premier League’s elite, though.
In 20 Premier League matches against United, Manchester City, Chelsea, Arsenal and Tottenham, Liverpool have only lost twice under Jurgen Klopp’s stewardship.
However, Liverpool will be without Sadio Mane who picked up a hamstring complaint on international duty with Senegal.
Attackers Philippe Coutinho and Roberto Firmino have now returned to training ahead of the crunch clash.
The duo’s participation in the match had been in some doubt.
They turned out for Brazil in the 3-0 win over Chile in the early hours of Wednesday morning.
Georginio Wijnaldum, Marko Grujic and Ragnar Klavan also reported back for training this morning having been on international duty.
United will be without Paul Pogba, Marouane Fellaini and potentially Michael Carrick.
Phil Jones could feature having missed England's World Cup qualifying wins over Slovenia and Lithuania due to a knee complaint.
