The Magpies aim to reach the last-eight stage of the competition for a fifth consecutive campaign when facing David Moyes' side at the Hill Dickinson Stadium (kick-off 7:45pm GMT).
Their reward, should they prevail against the Toffees, will be an away clash against the League Two side, who beat Arsenal via penalties following a 1-1 draw in last night's Round Four tie.
The quarter-final matches will take place on the week commencing Monday, 14th December.
**Carabao Cup quarter-final draw**
Fleetwood Town vs **Everton or Newcastle United**
Manchester City vs Bradford City
Crystal Palace vs Sunderland
Liverpool vs AFC Bournemouth