The study of nuclear electron capture (EC) offers an exciting alternative for the determination of the neutrino mass. Whereas only tritium and ¹⁸⁷Re can be used in the case of β-decay experiments involving the anti-neutrino, a potentially large number of EC-nuclides can be used in experiments involving the monochromatic neutrino. This alternative to β-decay experiments requires an accurate measurement of QEC-values of appropriate candidates. In the present work we initiate a search for such a candidate and determined the QEC-value of the electron capture in ¹⁹⁴Hg by direct mass measurements of ¹⁹⁴Hg and ¹⁹⁴Au. The new QEC-value of 29(4) keV determined by the ISOLTRAP Penning-trap mass spectrometer at ISOLDE/CERN forbids the K-capture for ¹⁹⁴Hg. However, it allows a determination of the neutrino mass by a combination of a micro-calorimetric measurement of the de-excitation spectrum from L-capture in ¹⁹⁴Hg and a comparable QEC-value remeasurement by high-precision Penning trap mass spectrometry.