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.
Saracens confirmed "one or more" staff members tested positive, but no players, and Harlequins said a "member of the club" was also among them.
The season was suspended in March and Premiership Rugby hopes to resume the league on the weekend of 15 August.
"We have to respect patient confidentiality so we won't be naming the person or people involved," Saracens said in a statement.
"The individuals will now go into isolation along with any others identified as close contacts in both their team and household settings. This is informed by protocols established with Public Health England (PHE) and Track and Trace."
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."