The draw for the next round was made today and they will face Northern League Division One side Shildon AFC should they beat Newport Isle of Wight.
The trip to County Durham would be a 540-mile round trip for the Yellamen with the tie being played on March 2.
Runcorn Town v Guernsey
Shildon v Newport (IW) or Ascot United
Spennymoor Town v Gornal Athletic
Larkhall Athletic or Tunbridge Wells v Hadleigh United