The Ground-based European Nulling Interferometer Experiment will combine the light collected by two or more VLT telescopes and make them interfere in a destructive way, thereby revealing the close neighborhood of nearby stars. Operating at mid-infrared wavelengths, GENIE will be particularly sensible to warm circumstellar dust. This paper presents simulated observations of the debris disk around the nearby A2V star zeta Leporis obtained with the GENIE simulation software. Parameters such as inclination, density power-law exponent and inner radius can be retrieved with a relative precision of 1% or better using only six observations of 15 minutes. In the context of the DARWIN/TPF mission, warm circumstellar dust could be a serious limitation to the detection of Earth-like exoplanets. This paper shows that GENIE will detect disks as faint as 23 times our local zodiacal cloud around Sun-like stars at 10 pc, and will thus allow to discard unsuitable targets for DARWIN/TPF.