Bodymoor Heath has been closed since last Thursday due to a severe coronavirus outbreak which has already seen the postponement of Wednesday’s match against Tottenham.
Villa have now raised concerns with the Premier League over a lack of preparation time for the Toffees visit, with fears the training ground may not open until Saturday at the earliest.
The league will now determine whether the match, already pushed back from Saturday, should go ahead. A decision is expected as early as Wednesday.
Nine players and five members of staff tested positive last week for coronavirus. Further testing took place over the weekend, with Smith and his squad continuing to self-isolate.
Villa have remained in dialogue with the Premier League and Public Health England, who will ultimately determine whether the outbreak has been contained.
Winger Trezeguet has revealed he is among the players to have tested positive for the virus.
The Egyptian international, who had missed a month with a hamstring injury, tweeted: “After rehabilitation and the beginning of the return to group training, I was infected with the coronavirus.
“Praise be to God for everything and may God heal every patient.”