The Shrews fought back to draw 2-2 with the Reds on Sunday and will be heading for Stamford Bridge if they can pull off an even bigger shock in the replay.
Holders Manchester City are also on their travels having been paired with Championship side Sheffield Wednesday, while derby rivals Manchester United face a trip to the winners of the replay between Northampton and Derby.
Oxford’s reward for a replay victory over top-flight Newcastle would be a trip to Championship leaders West Brom, while fellow League One side Portsmouth will face Premier League opposition at Fratton Park after Bournemouth and Arsenal resolve fourth-round matters.
Southampton or Tottenham will play host to top-flight basement boys Norwich, while either Coventry or Birmingham face a short trip to Leicester.
Championship sides Reading and Cardiff will battle it out for the chance to welcome in-form Sheffield United to their own stadium.
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Draw in full
Sheffield Wednesday vs Manchester City
Reading/Cardiff vs Sheffield United
Chelsea vs Shrewsbury/Liverpool
West Brom vs Newcastle/Oxford
Leicester vs Coventry/Birmingham
Northampton/Derby vs Man United
Southampton/Tottenham vs Norwich
Portsmouth vs Bournemouth/Arsenal