The Reds face Sir Alex Ferguson's side in the FA Cup fourth round at Anfield on Saturday with most of the pre-match centred around Patrice Evra's involvement
The previous meeting in October ended 1-1 but led to the eight game ban imposed on Luis Suarez for allegedly racially abusing Patrice Evra.
There are fears that following this controversy, the fierce rivalry will be more intense than ever, but Gerrard said the focus has to remain on the match, not individual players or isolated incidents.
"We do all have a responsibility - we all have a responsibility to ensure that this game is remembered for the football," he told reporters.
"Liverpool and Man United is a massive rivalry and, of course, there is going to be stuff in the papers and banter between fans.
“But it would be fantastic if, after the weekend, it is remembered for being a top game - and obviously, from our point of view, a Liverpool win.
Suarez is set to return from his ban on 11th February which coincidentally allows him to make his comeback in Liverpool's away game at Old Trafford.
The fallout from the incident with Evra led to both Sir Alex Ferguson and Liverpool managing director Ian Ayre issuing statements to the fans, messages that have been supported by Gerrard.
"We don't want any front page stories from this game, or any stories besides a football match between two top sides and may the best team win,” he added.