Hawks and Gosport both face difficult FA Trophy quarter-final ties after the draw was made.
Gosport Borough face a lengthy journey as they travel to Hull-based North Ferriby United of the Skrill North.
Lee Bradbury’s Hawks side host Aldershot, of the Skrill Premier, after their impressive win over Ebbsfleet.
The ties will be played on February 1.
Full draw as follows: Hawks v Aldershot Town; Eastleigh v Cambridge United or Luton Town, North Ferriby United v Gosport Borough, Grimsby Town v Tamworth or Chorley