His results are inconclusive, sources told ESPN's Adrian Wojnarowski.
The 59-year-old was already vaccinated and isn't experiencing symptoms.
However, Clifford isn't optimistic about his chances of returning that soon.
"I don't see a way that I coach tomorrow night," Clifford told reporters Saturday, according to The Athletic's Josh Robbins. "Monday, maybe. Then I guess if all these tests are negative it could be a chance by the time we go on the road."
Assistant Tyrone Corbin will assume head coaching duties if Clifford isn't given the green light for Sunday's game, according to Robbins.
Like Clifford, the Mavs bench boss received the COVID-19 vaccine and was asymptomatic.
Carlisle's test result was deemed a false positive the day after.