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City have been drawn at home to the Foxes who were playing Premier League football just two years ago.
The tie will take place on the weekend of November 7 and 8 at the MGroup Stadium.
The Hoops have won three matches in the competition already on their way to reaching the First Round Proper.
Ross Jenkins' side entered the historic tournament in the Second Round Qualifying, winning 2-0 away at Dorchester Town.
They then faced Enfield Town whom they dispatched with ease, winning 6-1 at home a day after the notable signing of former Watford and Sheffield Wednesday striker Fernando Forestieri was announced.
To reach the First Round Proper, City won 1-0 away at National League South side Torquay United thanks to a goal from in-form Scott Pollock.