The Spaniard was forced off with a hamstring problem after 27 minutes of Sunday's victory over West Ham at Upton Park.
While the injury is not considered serious, the Villa game may come too soon for the 26-year-old to recover.
Enrique told the club's website: "I am OK but I don't know if I'll be ready for the game. It's nothing bad but I don't know if I'll be able to play.
"I've had some treatment and then we will see. I hope I can be fit for the game."
After suffering from a knee injury early in the season that kept him sidelined, the Spanish star fell down the first-team pecking order but has recently been re-integrated into the side in a more advanced midfield role.
Brendan Rodgers' side are only four points behind city rivals Everton, who currently hold the final UEFA Champions League qualification spot, and the packed festive schedule gives them a chance to reduce the gap further.
"We will have many, many games. We have to think we can be there," said Enrique.
"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."
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