The cases are amongst the “workforce”, a statement said, and if confirmed would take the number at the club to four in the last four days.
Andre Villas-Boas’ side already cancelled a friendly on Friday against Stuttgart of Germany as a precaution.
Under health protocols adopted in recent weeks which are awaiting final approval, the four cases could mean Marseille’s scheduled opener against St Etienne on Friday may be called off.
At least 37 Ligue 1 players from 11 clubs have tested positive for COVID-19 in recent weeks.
The vast majority of them contracted the virus after resuming training in June, leading to quarantine and a flurry of cancelled pre-season matches.
With only one positive case announced, fellow top-flight sides Bordeaux, Dijon, Lens, Monaco and Nimes have not seen their preparations too disrupted.
On the other hand, Lille (with four cases), Saint-Etienne (five), Montpellier (six), Nantes (seven) and Strasbourg (nine) have all seen their pre-season affected.
Montpellier, Nantes and Strasbourg have had to cancel several friendlies.
“When the players become negative again, we will be able to use them. But in what state, I do not know,” said Strasbourg coach Thierry Laurey.
Two matches will not take place this weekend – between Paris Saint-Germain and Metz and the game featuring Montpellier against Lyon.
That is due to the Champions League semi-final commitments of PSG and Lyon in Portugal.
“Clubs have great fears over the resumption of the championship,” said one unnamed Ligue 1 president.
“We are afraid of being in the situation where for three months we had the car in the garage without being able to take it out, and when we finally can get back on the road there is a risk of it breaking down.”
Nice, meanwhile, have already decided to play their first match behind closed doors next Sunday against Lens.
If Marseille do welcome Saint-Etienne on Friday, it will be at a relatively quiet Velodrome where only 5,000 fans will be allowed.
Marseille’s request for an exemption to allow 20,000 people inside the ground was rejected by local government.