The Parkhead boss was responding following claims from Livingston manager David Martindale that the Scottish Premiership should bring forward its winter break to help curtail the spread of the virus among clubs and supporters.
Dundee, St Mirren and Dundee United have all reported positive Covid cases among their playing squad ahead of the weekend fixtures, and First Minister Nicola Sturgeon has urged fans to weigh up the risk of attending matches in the run-up to Christmas.
Postecoglou would prefer for games to go ahead as planned, but accepted others were better placed to comment.
"It is very hard to predict the future with this thing," Postecoglou stated. "We can have a break and we may find the worst is still ahead of the break and that puts more pressure on fixtures and clubs further down the line.
"My gut instinct is we keep playing until it is impossible to do so or we get advice that is best that we stop playing. But that is me talking with limited information.
"The paramount thing is the safety of our players and staff and supporters and we have to follow the guidance."