West Ham beat Wolverhampton Wanderers at the weekend to book their place in the last 32 of the cup competition, and Sullivan is hoping to avoid a Premier League team when the draw for the fourth round takes place later this evening.
The co-chairman insists that he wants West Ham to have a lengthy run in the FA Cup this season, and he feels that a tie against a lower league side would be ideal.
“We are now eagerly anticipating the draw for the next round and I would love to get Peterborough, Oxford, Colchester, Yeovil/Carlisle or something similar at the Boleyn Ground in the next round as we really want to go as far as we can in the FA Cup this year,” Sullivan said.
West Ham named a strong line up in their match against Wolves at the weekend, which highlighted how seriously they are taking the competition this season.
Slaven Bilic’s side left it late to secure the victory in the third round though, with Nikica Jelavic grabbing an 84th-minute winner.
Bilic has already gone on record to state that he would rather win the FA Cup this season than finish in the top four, which is a rare opinion for a manager to express in modern day football.
West Ham will be ball number three in tonight’s draw, which takes place at 7:00pm.