Brendan Rodgers' side are only four points adrift of city rivals Everton, who currently occupy the final Champions League qualification spot, and the packed festive programme gives them a chance to reduce the gap further.
"We will have many, many games. We have to think we can be there," Enrique told liverpoolfc.com. "We have beaten good teams this season. The teams at the top have been losing a lot of games so we have a chance.
"We're just four points behind the Champions League places and we have a big chance to be there before January finishes.
"We have to take it step-by-step. We have two games at home (against Villa and Fulham) now and we'll try to win them both.
"Then if we can get some good players in the transfer window, maybe we can do something."