United will play Steve Bruce’s West Bromwich Albion at The Hawthorns in the first round, with ties to be played in the week commencing August 8.
But their city rivals Wednesday were drawn the ball after United – meaning a first Steel City derby in some time was narrowly avoided, with the Owls paired with Sunderland in a repeat of last season’s League One play-off semi-final.
United reached the third round of the League Cup last season, beating Carlisle United and Derby County at home before going out on penalties to Premier League side Southampton at Bramall Lane.
Bruce is a former player and manager at United, with the Blades being the former Manchester United legend’s first managerial job. He later took charge of Wednesday.