The Spain striker is hoping that rivals Chelsea can do Manuel Pellegrini's men a favour by defeating the Reds at Anfield on Sunday
The Reds face Chelsea at Anfield on Sunday in a crucial clash at the top of the table where a win for the Blues could give Manuel Pellegrini's men a lifeline in the race for the title.
City would then be able to draw level on points with Liverpool, were they to win both of their games in hand, and Negredo is hoping Jose Mourinho’s side can help his side out.
"We know this is Liverpool's toughest game on paper,” he told Sky Sports' 'Weekend Warm-up'.
"But we are not going to give up the fight. So we want it to go in our favour and then, as I say, it is down to us to do our job by winning four games that will put us in a position where we have a chance."
Liverpool have won their last 11 games in a row to storm to the top of the table but Negredo is hoping their winning run does not continue.
"It's tough because it is not in our hands," he added. "We will battle until the end and you never know teams might slip up along the way somewhere and drop points themselves.
"There is still a lot of hope in the dressing room. While there are points available it is possible that other sides might make mistakes.
"We have to go all out to win every game. We have four left and we have to win them all and then sit back and see what happens."