City presently sit six points adrift of the high-flying Reds with a game in hand but, with Chelsea set to visit Anfield on Sunday, Negredo is optimistic that Jose Mourinho's troops can do his side a favour.
"It's tough because it is not in our hands," Negredo told Sky Sports News. "But we are not going to give up the fight. 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."
The Sky Blues travel to the capital for a clash with Crystal Palace on Sunday evening.