Goalkeeper Edwin van der Sar has not conceded in 1,302 minutes of league football, with the last goal scored against him on November 8.
But Allardyce will only be happy breaching United's defence if it means his side, currently 18th in the table, take at least a point from the encounter.
"I hope we can end the clean sheet record but it will be no good breaking that run if we don't get anything out of the game," he said.
"If we ended up scoring but didn't get anything out of it, I'd sooner we came off with a 0-0 because we would get something out of that.
"It is a challenge we should look forward to because no-one expects us to do anything so we have less pressure on us than we would have at Ewood Park."
Rovers have won only once in 21 league and cup visits to Old Trafford since 1963.
However, since Allardyce took over at Ewood Park in mid-December the team have not conceded a goal on their travels and the Rovers boss is hopeful that can continue.
But he also recognises the need to take their chances when they arise as he believes anything other than a defeat at Old Trafford would provide a boost to their relegation battle.
"If we got any positive result against Manchester United it would go a long way to helping us secure our Premier League survival," Allardyce said.
"Any precious point would almost feel like a win at this stage of the season with the form United are in.
"It would give the players a huge amount of confidence and belief in themselves to push their way out of the trouble they are in.
"Our aim tomorrow, as hard as it might be, is to go and keep our clean sheet mentality away from home.
"That is something to maintain but we must make sure we take care of the limited possession we get.
"If we frivolously continue to give the ball back to United without using the possession, it will be a difficult afternoon for us.
"If we can maximise our possession, we can at least assert a little bit of pressure on that back four and see if we can get a goal.
"It can be a lonely afternoon there for the front men but you can't afford to get one chance and miss it at Old Trafford.
"If you miss them, it is very rare you will get another one."
Allardyce believes the defending Premier League champions and current leaders will take some stopping on Saturday simply because of the security their frugal defence provides.
"There is no doubt this is the biggest challenge I have faced as Blackburn manager because of the position and form United are in," he added.
"The impregnable back line they have got does not concede a goal which means they only need one goal to win a game.
"Their attacking forces are allowed to go and attack because the defence is so good and that combination has brought them a huge amount of success recently."
Blackburn's hopes of keeping a clean sheet have been dented by the loss of centre-back Chris Samba to suspension while right-back Danny Simpson is ineligible to play against his parent club.
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