The Blades saw off Premier League Southampton at Bramall Lane on Tuesday night, and will face Spurs at their home ground in the second of the ties.
Spurs booked their last-four spot with a 4-0 demolition of Newcastle but will not necessarily relish a clash with lower-league opposition.
Nigel Clough's Blades went to Wembley in the FA Cup semi-finals last season, while the template in this tournament was set by Bradford going all the way to the final in 2013.
The other semi-final puts Liverpool up against Chelsea.
The Reds won 3-1 at Bournemouth on Wednesday night, while Chelsea put out a strong side to win by the same margin at Derby on Tuesday.
Chelsea boss Jose Mourinho won his first trophy in England by beating Liverpool to the League Cup in 2005, and his side will be away in the first leg.
"It will be a fantastic tie," Liverpool manager Brendan Rodgers told Sky Sports.
"If you want to win this competition you have to play against the good sides.
"The most important thing was getting through, but our performance was brilliant.
"We're into the semi-final, it's over two legs and it didn't matter who we got
We needed to get there, it's Chelsea and we look forward to it."
The ties are set to be played on January 20 and 21 and January 27 and 28.
Source : PA
Source: PA