The controversial striker has just three games of his suspension to go, and will return to action at the home of the Reds' greatest rivals at the end of September
|THIRD-ROUND DRAW IN FULL
Hull City Tigers
The striker was banned for 10 matches for biting Chelsea defender Branislav Ivanovic at the end of last season.
Suarez, who was convicted of racially abusing Patrice Evra by the Football Association in 2011-12, can expect a hostile reception from United fans on his return to action, should he be named in Liverpool's match day squad.
The 26-year-old scored against Port Vale in a behind-closed-doors run-out on Wednesday afternoon as he prepares to return to the first-team.
The Uruguayan had been keen to leave Anfield this summer, but is now resigned to staying with the club for one more season after Arsenal failed to seal his signature.
Elsewhere in the third-round draw, holders Swansea City were drawn away to Birmingham City, Manchester City host Wigan in a re-run of the FA Cup final, Chelsea travel to Swindon and Arsenal visit West Brom.