The Reds have failed to keep a clean sheet since their 4-0 win over Arsenal at the end of August. United, on the other hand, have scored 21 goals in 7 games and are undefeated so far this season.
But Thompson is confident Jurgen Klopp's can withstand United's attacking firepower and win the match.
"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.