One player and two staff at Watford and Burnley assistant manager Ian Woan are among six positive Premier League tests for coronavirus.
The other two are at a third club, the details of which have not been revealed.
Players and staff who have tested positive will now self-isolate for seven days.
It comes as squads started non-contact training on Tuesday, as the Premier League steps up plans for a restart.
A total of 748 players and staff from 19 clubs were tested. Norwich City did their tests on Tuesday.
Watford confirmed a player and two members of staff had tested positive but they would not be naming those involved as they had asked for medical confidentiality.
Before the news about Watford’s positive tests emerged, captain Troy Deeney said he would not return to training because he feared for his family’s health.
“We’re due back in this week. I’ve said I’m not going in,” Deeney, 31, told Eddie Hearn and Tony Bellew on the Talk the Talk YouTube show.
“It only takes one person to get infected within the group and I don’t want to be bringing that home.
“My son is only five months old. He had breathing difficulties, so I don’t want to come home to put him in more danger.”
Burnley said Woan was “asymptomatic” and “currently safe and well at home”.
“He will remain in close communication with club personnel regarding his re-engagement in training once he is clear of the virus,” the club added.
The Premier League has been suspended since 13 March because of the Covid-19 pandemic, with 92 fixtures remaining.