The borough issued the alert late last week after a water main break and flooding.
Authority Manager Carol Paul reported that water samples collected Sunday and Monday came back showing no evidence of bacterial contamination.
However, the Department of Environmental Protection would like samples collected for two more days before they will allow a lifting of the boil water advisory.
Paul, who says samples would be collected Tuesday and Wednesday, says that they expect those samples to come back good as well.
It is anticipated that the boil water advisory could be lifted Thursday.
The alert says that crews noticed cloudiness, or turbidity, in the water.
The Water Authority says that those most at risk for sickness include those with severely compromised immune systems, infants, and some elderly.
The Water Authority says that they have been testing the water for the presence of coliform bacteria and adjusting the chlorine levels to compensate for filtration problems.
All customers of the Greenville Water Authority are being asked to boil their water before consumption until the advisory is lifted.
Water that will be used for drinking, making ice, brushing teeth, washing dishes, or food preparation should be brought to a boil and allowed to boil for one minute.