The move would see a ban on the sale of alcohol both indoors and outdoors, and stricter rules on when pubs and restaurants can open.
It is understood that public health officials recommended the council areas be placed in Level Three following a marked increase in cases across the NHS Grampian health board region.
Scotland’s Covid-19 alert levels are reviewed every Tuesday morning by the Cabinet, before First Minister Nicola Sturgeon announces the results in an address to the Scottish Parliament.
Douglas Lumsden, co-leader of Aberdeen City Council, told BBC Scotland that Deputy First Minister John Swinney informed him that both Aberdeen city and Aberdeenshire could be moved to Level Three.
He said a move to Level Three would be "devastating" for businesses in the region.