Mathematician Benitez believes one win against United could win Reds the title

Such has been Liverpool's dreadful recent record against the champions, that even co-owner Tom Hicks suggested after December's home defeat that the Reds did not look as if they believed they could beat their rivals.  

It is certainly a matter of worry for fans and seeing United win their 17th league title - one short of Liverpool's record - and reach another European Cup Final has heightened the concern.  

Unhappy hunting ground: Javier Mascherano is sent off as Liverpool fall at Old Trafford earlier this year

Benitez accepts the problem and told the LFC magazine: "If you beat Manchester United once it results in a six-point swing either way and that can be the difference."  

Liverpool finished 11 points behind the champions this season and Benitez wants his team to be hungrier next term.  

"Clearly, just one team can win the league, so it doesn't really matter if you are three, six, nine or 11 points behind as we are this season," said the Spaniard. "It is not a massive difference. It may just come down to one game over the course of a season. 

"The key for me is knowing there is a difference between us and the three teams above us and that we must now reduce this gap. It was not massive this season. We came closer than last season. Hopefully next season we will be closer again, maybe even on top of them."  

Benitez has so far made just one summer signing, Philipp Degen from Borussia Dortmund on a free transfer, and said: "This club is all about winning things so we are disappointed not to have picked up any trophies this season.  

"But we will be hungrier next season. Clearly, we are winners and want to win silverware every year. We have not done that for two seasons so we will be looking to improve again in order to try and deliver something for our supporters next time." 

Despite an end-of-season run that saw them lose just two of their 19 games, one of those defeats was a painful 3-0 mauling at Old Trafford. In Benitez's four seasons at Anfield, Liverpool have lost seven of their league clashes with United, with a 0-0 draw their only point in that time.

Benitez's only victory against them was a 1-0 FA Cup fifth-round success in 2006.   Benitez will now focus his attention on summer transfer targets but he may have to sell as well.  

There is strong speculation in the Italian media that Juventus are trying to sign midfielder Xabi Alonso for £12million.  

Benitez still hopes to use £6million-rated goalkeeper Scott Carson as a makeweight in a deal to bring Aston Villa's Gareth Barry to Anfield, while Fulham are believed to be interested in re-signing Steve Finnan for £2million.  

Benitez is also trying to land Bordeaux's veteran goalkeeper Ulrich Rame, with the unimpressive Charles Itandje moving in the opposite direction.