The Reds have lost their last four games against Louis van Gaal’s side, including a 1-0 defeat in the Premier League on Merseyside in January.
However, Jurgen Klopp’s men have won their last three Premier League games and created history with a last-minute winner to come from behind with 10 men and beat Crystal Palace on Sunday.
Former Liverpool defender Jones, who was part of Graeme Souness’s FA Cup-winning side in 1992, is confident the five-time European Cup winners can secure a commanding first-leg lead with home advantage on Thursday night.
“When we played Manchester United at home this season, we went right at them,” Jones told The Sport Review.
“We shocked them and didn’t let them play. We were the better team even though it was 1-0 in the end. We were the much better team.
“The atmosphere on Thursday will be electric. I’d expect Liverpool to come out of the traps quick and I’ll go for a 2-0 win.
“It won’t be as easy at Old Trafford. If I’m right, we’ve got a great chance at Man Utd.”
Enhanced odds: Get 7/1 on Liverpool to beat Man Utd
Liverpool are in sixth place in the Premier League table and six points behind fourth-placed Manchester City.
The Reds haven’t won Europe’s second-tier competition since 2001 when Gerard Houllier’s side were 5-4 winners against Alaves.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news