Everton's meeting with Manchester City was called off hours before kick-off after the Citizens reported a spike of positive cases.
The Athletic are reporting that the most recent round of testing returned "a number" of positive tests at Fulham that could lead to their clash with Spurs being called off.
That figure surpassed the previous highest figure recorded - 16 for 9-15 November - though the percentage of positive cases was lower.
The 2019-20 season was played to a completion earlier this year following a 100-day shutdown as a result of the pandemic, but prior to the season being restarted, the prospect of the table being decided by average points-per-game, or even being declared null and void, were discussed by the 20 Premier League clubs.
"The Premier League can today confirm that between Monday 21 December and Sunday 27 December, 1,479 players and club staff were tested for COVID-19", the league said in a statement.
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Rochdale are one of the League One clubs affected and their club doctor described the continuation of the season in the current climate as "not the wisest thing".
The Telegraph reports that chairpersons have discussed a potential mid-season break, to help alleviate concerns around the spread of the virus. "No specific details as to clubs or individuals will be provided by the League and results will be made public after each round of testing".
City's trip to Chelsea on Sunday, as well as their Carabao Cup semi-final against Manchester United on January 6, is also in doubt, although the picture at the Etihad will become clearer on Wednesday when the results of tests done on Pep Guardiola's squad Tuesday are confirmed.
All remaining seven Premier League games on Tuesday and Wednesday are still set to go ahead.
"I think the Premier League and clubs have done a great job to keep football going in hard circumstances, so let's hope we can keep it going".