The north west giants meet in a potentially explosive Barclays Premier League clash at Old Trafford at lunchtime.
The game could see United defender Patrice Evra and Liverpool forward Luis Suarez face each other for the first time since the race row which erupted last October.
In a joint interview with United Review, Charlton and Callaghan have spoken of the respect they have for each other's clubs - the two most successful in English history - and they hope that can shine through.
Callaghan, 69, who made a record 857 appearances for Liverpool, said his message to fans would be: "Go and enjoy the football. Enjoy the success that both clubs have had.
"Well, we haven't had much lately, but just enjoy being a fan of one of these two great clubs."
Charlton, 74, United's record scorer with 249 goals, said: "They're lucky that the clubs have had good managers, coaches and players, so that it's been a pleasure to go and watch both teams.
"There is a respect there, and we must never forget that."
The pair acknowledge that the rivalry has become increasingly bitter in recent times but point out the clubs have a lot in common.
They also comment on the disasters of Munich and Hillsborough and how both clubs should pay their respects to each other.
Charlton said: "The majority appreciate that both Munich and Hillsborough are put in a place of respect - you mustn't do anything to disrespect those who died."