Liverpool have 18 championships under their belts with United just one behind.
The Reds have not won English football's top tier since the 1989/1990 season while Sir Alex Ferguson's men have won it 10 times since then.
Spanish star Torres is desperate to stay ahead of United and insists it is Rafa Benitez's biggest priority this season - ahead of even the Champions League.
Torres said: "Manchester United are pressing us and if they win the league they will have the same number of titles as us.
"That would be a small tragedy for us all. We are playing game by game but if the truth be told the club and the fans are more aimed at winning the Premier League.
"The title has not been won for 19 years and there is a lot of excitement at the moment.
"We will never give in and we will fight for the title until the last minute."