The Premier League side said a large number of first-team players and staff are in isolation after returning positive tests on Monday.
Dean Smith’s side is scheduled to face Liverpool on Friday night.
“Discussions are ongoing between medical representatives of the club, the Football Association and the Premier League,” Villa said in a statement.
Southampton’s FA Cup third-round game against Shrewsbury on Sunday was called off earlier on Thursday after a significant number of Shrews players and staff tested positive for COVID-19.
Rooney and Derby’s first-team squad will miss their FA Cup tie at Chorley on Saturday following a Covid-19 outbreak which closed their training ground on Monday.
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