The Barclays Premier League encounter at Anfield on Sunday will be Liverpool's first home match since the publication of a damning new report into the Hillsborough disaster.
A number of tributes are being planned prior to the game to commemorate the 1989 tragedy, remember the 96 victims and acknowledge the fight of their families to find the truth over its cause.
Since the report there have also been widespread appeals to fans of all clubs to cease tasteless chanting about tragedies to have befallen their rivals.
United have been at the forefront of those calls and it is hoped chants relating to Hillsborough, or the Munich air disaster which badly affected the Old Trafford club, will never be heard again.
United boss Sir Alex Ferguson has been especially forthright in his comments on the matter and Rodgers has acknowledged such support.
Rodgers said: "There has been dialogue all week. There is respect in terms of the traditions of both clubs.
"We want this day to be remembered for the right reasons before the game, and the footballing reasons.
"A lot of work has been done and hopefully Sunday will pass off peacefully and well and we can talk about the tributes and football.
"It is an emotionally-charged game. I wouldn't sit here and tell Liverpool supporters how to behave. I know how they have behaved over many years has been fantastic.
"These are well-educated supporters who value humanity. I have no issues or no problems there, the message has been clear, and from Sir Alex as well, in relation to his supporters.
"I am sure once we pay the tributes to the families we can get on with the football."
One side issue to have reoccurred is the race row between Luis Suarez and Patrice Evra which overshadowed Liverpool's campaign last season.
Suarez was banned for eight matches for racially abusing the United left-back during the corresponding fixture last October and the pair did not shake hands before the return match at Old Trafford in February.
The Premier League's pre-match handshake ritual has been under scrutiny for other reasons of late, but Rodgers is not expecting any more issues on Sunday.
He said: "I think enough has been said and written about that over the last year.
"This has been ongoing and everything to say about this has been said. There is nothing else I can add other than you just move on.
"I said when I first came in here, it was an episode that just went right through last season. It is a new season, another game. We look at both sets of players to respect it.
"Having worked here with Luis Suarez over the course of the last few months, he is a good guy, a good man. Ethically he is very strong, so I am sure there will be no problems at the weekend."
Asked if he was confident the pair would shake hands, Rodgers said: "Very."
The club's managing director Ian Ayre has also played down the significance of the gesture.
Ayre told talkSPORT: "We will be doing a handshake as there always is and, as regards to the Luis Suarez-Patrice Evra thing, I think it's just a non-story for this day.
"Despite what the media says, nobody has gone and told Luis Suarez what to do.
"Luis is a grown up, as I'm sure is Patrice Evra, and I think those players, like every other player on the pitch that day and everybody in the stadium, will recognise this isn't a day to talk about who is going to shake whose hand.
"This is about everybody being together for a much more important cause."
A mosaic will be displayed by fans around three sides of the ground prior to the game, while 96 balloons will be released by captains Steven Gerrard and Nemanja Vidic among other tributes.
Kenny Dalglish, manager at the time of the disaster, is also expected to return to Anfield for the first time since his second spell in charge ended last May.
Rodgers said: "There is no doubt there is a big emotion throughout.
"Liverpool-Manchester United games are always very emotional. You add to that the findings of the last couple of weeks and it makes it even more emotional.
"First and foremost, we want to pay tribute to the families, the victims and the survivors. It is our chance to do that.
"After the fight of the last 23 years, it is the very least we can do."