Singularities in multi-stream flows of relativistic plasmas can efficiently produce coherent highfrequency radiation, as exemplified in the concepts of the Relativistic Flying Mirror [S. V. Bulanov, et al., Phys. Rev. Lett. 91, 085001 (2003)] and Burst Intensification by Singularity Emitting Radiation (BISER) [Pirozhkov, et al., Scientific Reports 7, 17968 (2017)]. Direct observation of these singularities is challenging due to their extreme sharpness (tens of nanometers), relativistic velocity, and transient nonlocal nature. We propose to use an ultrafast (a few light cycles) optical probe for identifying relativistic plasma singularities. Our Particle-in-Cell (PIC) simulations show that this diagnostic is feasible.