If the game is postponed it would present a further fixture backlog for Spurs, who remain in the Europa League, the FA Cup and Carabao Cup and have already had their match against Fulham on December 30 postponed for the same reason.
It is understood Fulham have been approached about playing Spurs this Wednesday. However, this would represent a significant and disruptive challenge for the west Londoners after their own Covid outbreak.
The Cottagers also played 120 minutes in the FA Cup against QPR on Saturday and face near-neighbours Chelsea on Friday.
Villa were forced to close their Bodymoor Heath training ground last Thursday and fielded a blend of under-23 and under-18 players in their FA Cup third-round defeat to Liverpool the following day.
Spurs boss Jose Mourinho said he was preparing to face Villa on Wednesday unless told otherwise.
Speaking after his side's FA Cup victory over Marine, the Portuguese said: "Nobody told me that I'm not going to play so (on Monday morning) we start to prepare for that game, and the same Tuesday unless somebody tells us different."
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