The NCAA announced Tuesday that five positive COVID-19 cases have been identified out of 2,300 tests conducted so far this week ahead of the NCAA Tournament. Those tested so far include members of team's traveling parties -- not just players and coaches -- as well as officials from the NCAA. The positice case count of five is up from zero positives that had been identified as of Monday.

Because of the breadth of who has been tested, NCAA senior vice president of basketball Dan Gavitt reiterated that it shouldn't be assumed the positive tests came from players or coaches.

"An assumption shouldn't be made about any individuals, or even any groups, because the overall testing numbers include both official travel parties of the teams as well as working staff and committee members," Gavitt said.

Additionally, Gavitt said tournament officials are not expecting to need one of the four replacement teams on standby in the event of a team needing to drop out due to COVID-19. 

"We are not anticipating that right now," Gavitt said Thursday afternoon. "But again, we are living in a pandemic. So we do take things day to day, and even hour to hour. But fortunately, we are not aware of any situations that would result in a replacement team coming in."

Later, Tuesday's 6 p.m. Eastern deadline for a replacement team to be chosen passed without Louisville, the top replacement team, being contacted, a source told CBS Sports' Matt Norlander. With no teams forced to withdraw from the tournament, it essentially "locks."

Gavitt confirmed that 67 of the 68 tournament teams have arrived, with Virginia as the lone exception. The Cavaliers were forced to withdraw from the ACC Tournament last week due to a positive COVID-19 case but are expected to arrive in time to complete the necessary protocols to play their first-round game Saturday night against Ohio.

The Cavaliers have been planning to arrive in Indianapolis on Friday, but Tier 1 personnel must register seven consecutive negative tests before arrival. Once on site, Tier 1 personnel must register an additional two consecutive negative tests on separate days before leaving quarantine. That timeline would mean the Virginia personnel that make the trip will be getting out of quarantine some time in the hours before their scheduled 7:15 ET tip against Ohio on Saturday.