In a release the Highlanders said they had cancelled today's training session, but at this point there has been no decision made on Friday's game in Dunedin.
They said there had been no change to the rest of their schedule this week.
The Highlanders have managed to play four games so far this season, losing all four of them.
However, another postponed game would be a major setback for Moana Pasifika, who have played just one game so far.
They had two games postponed at the start of the season because of Covid-19 in their camp.
They were then beaten by the Crusaders before their game against the Hurricanes last weekend was postponed as the Hurricanes preparation had been disrupted by Covid-19.
The Blues also released a statement confirming that Covid-19 was further impacting their squad.
They were currently working through the full impacts of this situation, including in regards to Saturday's fixture against the Crusaders in Christchurch.
The Blues said both the Crusaders and New Zealand Rugby were fully aware of the current situation.
They hoped to speak further on developments by tomorrow (Wednesday).
The Blues have also postponed all planned media interviews with players set for today.
The Highlanders played in Auckland against the Blues last weekend, with a number of the Blues players forced to withdraw from the team following positive tests.