The league has announced that between Monday, February 22 and Sunday, February 27, a total of 2,733 players and club staff were tested.
It is the fourth week running that the round of twice-weekly testing has produced just two positive tests.
The Premier League have confirmed two positive Covid tests in their latest round of testing
Those who have tested positive will now have to self-isolate for a period of 10 days.
The news comes a little over a week after Manchester United became the latest club to be hit by a Covid outbreak.
The Old Trafford club received positive results among three of their backroom staff, with the majority missing from the dugout during their victory over Newcastle.
No players were affected, while Ole Gunnar Solskjaer had more staff back around him during Sunday’s 0-0 draw with Chelsea at Stamford Bridge.
Man United’s game at Chelsea went ahead with no issues despite an outbreak last week
Last week it was confirmed that Premier League players and coaches will be required to isolate for 10 days following any overseas trip, complicating the schedules of teams still in the Champions League and Europa League.
Outside of training and competing, a mandatory 10-day quarantine will now be required for all overseas trips for club or international football.
But the 10-day period can be reduced by half if a player of staff member can provide a negative Covid-19 test following a five-day isolation.