Town are in the second round of the cup for the first time in ten years, after defeating Brighton 3-2 in extra time this week.
The last time the Shrews took on the Blades, also in the League Cup, they suffered two 3-0 defeats in the first round in 1999. Town's last victory was in 1987.
Neil Warnock's men are currently second in the nation's second tier, having won three of their four league games. Sheffield United dispatched Boston 1-0 in the previous round, a team who Town have already encountered this term.
It is likely that boss Gary Peters will delay focussing on the cup draw until after Town's double header against Wycombe and Leyton Orient.
Peters has already made it clear that any progress and financial reward from the competition is a bonus, and he is fully focussed on the league.