Six players and four non-playing members of staff have tested positive after the first round of Premiership Rugby's coronavirus testing.
A total of 804 tests were carried out across the 12 clubs on Monday.
Northampton Saints have confirmed that one player has tested positive, while Saracens, Harlequins and Worcester say members of their staff are affected.
The season was suspended in March and Premiership Rugby hopes to resume the league on the weekend of 15 August.
"We can confirm that one or more members of staff at our club have tested positive in our PCR Covid-19 screening programme in the round of tests taken across the Premiership on Monday 6 July," Saracens said in a statement.
"We have to respect patient confidentiality so we won't be naming the person or people involved.
Worcester, meanwhile, say two members of staff have tested positive.
"Both are asymptomatic but, as part of the procedures introduced by Premiership Rugby as part of Stage Two of the Return to Training Protocols, they will be re-tested. Both are currently self-isolating at home," the Sixways club added.
Premiership teams were told at the start of June that they could begin socially-distanced non-contact training in small groups, and were able to progress to close-contact training from Monday onwards.
Leicester Tigers and England scrum-half Ben Youngs told the BBC: "I'd probably be naive to think that out of 800 tests you aren't going to get a few [positives].
"But I think what's important are the protocols of what happens next. You don't want that 10 to be 30 next week, then 80, and then we are in a spot of bother.
"But rugby does need to get back up and running. The clubs need it, everyone needs it, so we need that to be as diligent as possible across all the clubs to allow that.
"Hopefully people follow the protocols to make sure next week it isn't any larger than that."