The Whites secured passage into the third round of the tournament with a 3-0 victory over Crewe Alexandra at Elland Road on Tuesday night.
A goal from stand-in captain Kalvin Phillips followed by a double from wide man Jack Harrison was enough to see off the League One visitors in front of a sold out crowd in LS11.
United have now been handed an away tie with Championship outfit Fulham at Craven Cottage in the capital as a result.
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The only time the two teams have met previously in the League Cup competition was during in the 1969/70 campaign. Leeds defeated their London counterparts 1-0 as club legend Jack Charlton bagged the winning goal.
Third round ties are due to be played on the week commencing September 20.