The Argentina international, plagued with injuries in recent years, will be out for between four and six weeks after damaging a muscle at the back of his thigh on Wednesday's in the 7-1 aggregate King's Cup win over third-tier Ceuta.
Spain centre-back Gerard Pique is suspended because of his red card at Getafe last weekend and, after Rafael Marquez and Dmytro Chygrynskiy were sold on in the close season, Guardiola's options are limited.
Brazilian defender Maxwell, who typically plays at left-back, said on Thursday it would be better to give a youngster from the B team a chance rather than draft him in to partner captain Carles Puyol in the centre.
"I like being on the pitch and helping the team and I am available to the coach," Maxwell said at a news conference.
"But it's definitely better to put one of the young lads from Barca B in the centre than Maxwell," he added.
Teenager Marc Bartra, who played both legs of the King's Cup last 32 tie against Ceuta, trained with the first-team squad on Thursday and could start against Villarreal, who are third in the standings, two points behind champions Barca in second.
Undefeated Real Madrid are top on 26 points, one ahead of their Catalan arch-rivals, with the two to meet in Barcelona at the end of this month in the first "Clasico" of the season.
TERRIBLE REFEREE
Real coach Jose Mourinho will probably be forced to watch their match on Sunday at mid-table Sporting Gijon from the stands after he was sent from the bench during Wednesday's 5-1 Cup win over third-tier Real Murcia.
Local media reported that the flamboyant Portuguese had verbally abused the referee in Spanish after being told to calm down, using a phrase roughly equivalent to "go to hell".
"I am not saying the referee was bad," Mourinho told a news conference after Wednesday's game, before listing statistics purporting to show the large number of cards the referee had handed out during his career.
"I am a terrible referee but anyone could have officiated at this match without any problems," Mourinho added.
The disciplinary committee is due to meet on Friday.
In other matches, fourth-placed Espanyol play at struggling Racing Santander on Sunday and Valencia, in fifth, host Getafe in Sunday's late kick-off. Sixth-placed Sevilla are away to Real Zaragoza on Sunday.
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