The meeting had already been arranged between chairman John McKenzie and powerbroker and vice-chairman of the plc board Allan Leighton, but it is thought Reid's position would be added to the agenda.
Leeds are third from bottom of the Premiership following their worst start to a campaign for 22 years.
After three straight defeats, culminating in the 4-0 loss at Everton, his position is looking increasingly precarious, despite keeping The Whites in the top flight last season.