If your potentiometer (wired as a rheostat) is, say 1kohm, and it is wired in series with the internal resistance of the DMM (say 10Mohm = 10000k), and with series with a 10V source for example, the voltages you read for both end positions of the wiper will be:
V1 = 10V * (10000k/(1k+10000k)) = 9.999V
V2 = 10V * (10000k/(0k+10000k)) = 10.000V
With a 100kohm potentiometer:
V1 = 10V * (10000k/(100k+10000k)) = 9.901V
V2 = 10V * (10000k/( 0k+10000k)) = 10.000V
With a 10Mohm potentiometer:
V1 = 10V * (10000k/(10000k+10000k)) = 5.000V
V2 = 10V * (10000k/( 0k+10000k)) = 10.000V