The young Foxes will first face the Citizens at their Academy Stadium on Wednesday 11 March before the return leg at King Power Stadium on Wednesday 8 April, with both ties scheduled for 7pm kick-offs.
City dispatched Wigan Athletic, Chesterfield, Southampton and Birmingham City to reach to the last-four of the competition for the first time in 28 years.
Man City, meanwhile, beat Oxford United, Coventry City, Stoke City and most recently Crewe Alexandra to advance to the semi-finals.
Ticket details and prices for the tie at King Power Stadium will be released on LCFC.com in due course.