The scheme began on May 17 and have now been repeated on a further three occasions, with just one positive announced on Wednesday from nearly 1,200 tested.
Players from other clubs would likely also miss their first game should they return a positive test in the second batch on Friday - if, as expected, the Premier League confirms its first full round of fixtures will take place as expected on the weekend of Saturday, June 20.
The Premier League has revealed that its latest round of testing has thrown up a single positive case of coronavirus.
It is as yet unclear whether the positive test result came from one of the club's players or from a member of staff.
As part of preparations to return to action, England's top flight is carrying out extensive screening of players and staff from across the league.
The Premier League is providing this aggregated information for the purposes of competition integrity and transparency.
The latest round was the first to take place since clubs unanimously agreed a return to contact training, and the last before the government gave the all-clear for live competitive sport to return behind closed doors in the United Kingdom on Monday.
They went on to say: 'They are currently asymptomatic and will now self-isolate for seven days, in line with Premier League protocol, before undergoing further testing.
"We shall continue to strictly adhere to the Premier League's Return to Training protocol, which ensures our Training Centre remains a safe and virus-free working environment".
There have now been five rounds of testing for Covid-19, and the total of positive results has increased to 13 from 5,079 tests.