United did the double over the Reds last season, Rodgers' first in charge at Anfield, but Liverpool head into Sunday's encounter full of confidence after winning their opening three fixtures this term.
"There's an intense rivalry there," said Rodgers. "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.
"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."
Liverpool v Manchester United kicks off Sky's Ford Super Sunday coverage beginning at 12.30 on Sky Sports HD 1 and on Sky 3D.