Vieira revealed on Christmas Eve his side has suffered a "couple of cases" but that outbreak has reportedly worsened over the past 48 hours.
However, it has not been deemed sufficient by the Premier League for the game to be rescheduled.
Clubs were told at a meeting on Monday that games will go ahead if each team has 13 fit outfield players and a goalkeeper.
At the same meeting, the English top flight clubs rejected the option of temporarily halting the season to allow a circuit breaker for infections.
Three games scheduled for the traditional round of matches on December 26 have already been called off due to squads decimated by Covid-19 infections and injuries.
Postponements to Leeds' trip to Liverpool, Everton's clash with Burnley and Watford's visit to Wolves have taken the total number of Premier League games called off over the past two weeks to 13.
Across the three divisions below the Premier League, 22 matches in the English Football League (EFL) scheduled for Boxing Day have already been postponed.
No restrictions have yet been put in place for the size of crowds at matches in England, although supporters do have to provide proof of vaccination or a negative test taken in the previous 48 hours.
Sport in Wales will be forced back behind closed doors from today, while in Scotland a restriction of 500 outdoor public events has seen Scottish Premiership clubs bring forward their winter break by a week after Sunday's fixtures.
Crystal Palace Premier League Patrick Vieira COVID-19