Agger relishing run-in
This season, sitting second seven points behind Chelsea with a match in hand, represents their best chance of ending that long drought since 2009, when they ran United a close second.
Agger, one of the few survivors from that 2008-09 campaign, is confident they can deal with expectations.
"When you play for Liverpool Football Club there is always pressure and that won't change between now and the end of the season," he told the Liverpool Echo ahead of Sunday's trip to Old Trafford.
"Part of playing for this club is being able to handle that pressure. I think the players here have proved over the course of this season that they are more than capable of doing that.
"We have had some great results and there have been a few times when we have been all the way up there at the top.
"We are in a good position, but we are only in March. There is still a long way to go and a lot of points to play for.
"We haven't achieved anything yet and we need to keep going over the final 10 games.
"We have some big games against teams close to us in the table. They are games we have to win."
Agger's future seems to be a subject for annual speculation and, after he was taken off in the 4-3 home victory over Swansea, that began again.
But the Denmark captain played the full 90 minutes in the win at Southampton the following week, and reckons he took it all in his stride.
"There was no extra motivation. I am always motivated when I am on the pitch," the 29-year-old added.
"Did I speak to the manager about why I was taken off against Swansea? No. That's football and you get on with it.
"The clean sheet against Southampton was good - not only for me, but for the team.
"The result lifted everyone and now we're preparing to face Manchester United."
Manager Brendan Rodgers has always been reluctant to talk up his side's chances, and he agrees with Chelsea counterpart Jose Mourinho - who not so long ago claimed the Reds were favourites for the title - that it is Manchester City's to lose despite currently being fourth, nine points off the top but with a superior goal difference to the rest of the top four.
"He (Mourinho) is right in saying Manchester City are the club that has the power in terms of squad. They have three games in hand. Win them and they go the top - and they will expect to win them," the Northern Irishman told talkSPORT.
"I have learned a lot from Jose (previously working under him at Chelsea). He is a great man and we remain close but we are two different people. I have never made a big push publicly about us winning the title.
"It is not about playing down expectations or mind games - it is just about taking a humble approach to the season and how we have worked and because the players are doing all the talking on the field."
That was reflected when the squad returned to training this week, having been given five days leave.
"It was interesting, really, as we had an adaptation day after they had been off for a few days," Rodgers added.
"It was supposed to be a low-intensity session but the quality and the intensity they worked at was incredible. I actually had to take them off it a little bit.
"Sunday is a game we are really looking forward to. For us, it's about retaining the focus.
"We know it's a big game, but we've done well in a lot of the big games this season."
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