Sir Alex's men know all too well what happened last season when United were eight points clear with six games to play and still lost out to the Blues in the title race, albeit in dramatic fashion, on the final day of the campaign.
While happy to be setting the pace at the Barclays Premier League summit, Fletcher says the Reds are firmly focused on maintaining their lead by putting together a lengthy run of victories.
"We do feel this Christmas period, if we go on a good run of winning games it would really put us in a good position. Come the New Year then we can then really kick on," the Scot told PA Sport.
"We have been in this position before - we were eight points in front of them last season with far fewer games to play and we didn't win the title. We can't take anything for granted and look at the league table and think we are in a comfortable position. We use the experience of last season to realise that is not the case.
"The manager speaks about going on runs of winning matches - that is what we will try to do now. We have to kick on and win as many games as possible. If we can do that we'll find ourselves in an even stronger position."
In order to help gain the current advantage over City, the Reds have had to produce a string of memorable comebacks of the highest order, not least because clean sheets have been, surprisingly, very hard to come by this term. Nevertheless, Fletcher insists never giving up is something that has always been and always will be part of the team's make-up.