In most unconventional superconductors, the importance of antiferromagnetic fluctuations is widely acknowledged. In addition, cuprate and iron-pnictide superconductors often exhibit unidirectional (nematic) electronic correlations, whose fluctuations may also play a key role for electron pairing. In these materials, however, such nematic correlations are intertwined with antiferromagnetic or charge orders, preventing the identification of the essential role of nematic fluctuations. FeSe1-xSx is an ideal candidate system to search for such magnetic fluctuations which, unlike other iron-based families, do not exhibit competing or coexisting orders. Here we propose to perform a combination of zero-field and longitudinal-field µSR measurements on single crystals of FeSe1-xSx (x = 0, 0.14, 0.17, 0.2) and investigate magnetic instabilities which arise in the nematic states of these materials.