The Stoke beat Hamble ASSC 4-0 away from home in the Second Round but are currently struggling around the basement of the Blue Square South, only picking up their first win this Saturday when they defeated Bromley 2-0 away from home.
At the Camrose the club have lost four of their six home league games so far and will be keen to improve their season with a victory against The Shots.
Matches are due to be played on Tuesday 9th December.
The full draw:
Lymington Town vs Fleet Town or Fareham Town
Petersfield Town vs Andover
United Services Portsmouth vs Bashley
Gosport Borough vs Farnborough
Basingstoke Town vs Aldershot Town
Eastleigh vs Totton & Elding
Blackfield & Langley vs VT
Brockenhurst vs Hayling United