The Gunners, who defeated the Lady Pies 3-0 to lift the Trophy in Rotherham last November, beat Reading 3-1 on Saturday to reach this stage.
Notts, meanwhile, progressed by seeing off Yeovil Town by the same margin, with England striker Ellen White bagging a brace.
Giant-killers London Bees, who ousted FA WSL champions Chelsea with a stunning penalty shootout victory, must travel to Sheffield FC, 2-0 victors against Bristol City.
2014 Cup winners Manchester City are at home to Doncaster Rovers Belles, and will be brimming with confidence after defeating Aston Villa 8-0 on Saturday. Donny booked their last-eight berth by seeing off Sunderland.
Finally, Liverpool’s reward for a derby win over Everton is a trip to Birmingham City, who dispatched Oxford United 2-0.
This season’s FA WSL Continental Tyres Cup Final will be played on Sunday 2 October (3pm KO) at Manchester City’s Academy Stadium.
The FA WSL Continental Tyres Cup quarter-final draw (home sides first):
Sheffield FC v London Bees
Birmingham City v Liverpool
Manchester City v Doncaster Rovers Belles
Arsenal v Notts County
Ties to be played on 6-7 August