Last season - Rodgers' first in charge of the Merseysiders - their encounters in the league with United saw them lose both at home in September and away in January, 2-1 on each occasion.
But Rodgers has emphasised his feeling that his team were unfortunate to be defeated in the first game and also pointed to the similarities in the top-flight records of the two clubs since they last met as reason for encouragement ahead of the Anfield encounter on Sunday.
Asked about the meaning of the fixture, Rodgers - whose side have won all three of their matches so far this season, overcoming Stoke and Aston Villa in the league and Notts County in the Capital One Cup - said: "There's an intense rivalry there.
"It's not just the football clubs - it's the cities that you're representing.
"It's a game that, last year, we were unfortunate not to get something from. We lost the game but we're very confident going into this game.
"It's a game which should be very close. We're at home and we'll look to take the initiative."
He added: "If you look at our numbers since we last played Manchester United in January, that's the improvement where we've really kicked on. The big thing for us was consistency.
"From when we played them in January, we've played 18 Premier League games each - they have won 11 and we have won 10, we have drawn six games and they have drawn five, and we have both lost two games.
"So over the course of that period from January they have made two points more than us and obviously they became champions.
"For us, it's a case of continuing with that consistency. If we can do that, I think we can compete with anyone.
"We know it's a really difficult challenge but we've shown enough in the last number of months, the second half of last season and the beginning of this season, that we can sustain a challenge. That's something we're very determined to do."
United have so far this term beaten Wigan in the Community Shield and Swansea in the league before drawing with Chelsea.
Liverpool centre-back Martin Skrtel is set to make his return to action in Sunday's contest.
Skrtel, yet to feature this season, is available after recovering from a knee problem, but full-back Aly Cissokho will play no part in the game after picking up an ankle injury against Notts County on Tuesday that Rodgers says could see him sidelined for "four to six weeks".
Two other Liverpool players who came off injured in that match, defender Kolo Toure (groin) and midfielder Joe Allen (hamstring), are both doubts for Sunday.
Striker Luis Suarez misses out again as he continues his suspension, although he could face United at Old Trafford in the Capital One Cup third round next month as his 10-game suspension will then have been completed.
Regarding Suarez, Rodgers said: "He has been working very hard in training and he played a game behind closed doors.
"The focus is purely on getting him up to match fitness by the time he is available."
Meanwhile, Rodgers was refusing to give anything away at his pre-United press conference on Friday afternoon regarding various players Liverpool are reportedly trying to sign ahead of Monday's transfer deadline.
The manager was asked about five reported targets in Tiago Ilori, Andriy Yarmolenko, Shay Given, Mamadou Sakho and Victor Moses.
He said: "You guys keep asking and we as managers have to give the same answers to you.
"You are better to say nothing until the player is in the building.
"Until that point it is only ever speculation."