The search for the ferromagnetic quantum critical point (FM QCP) has always been a captivating research topic in the scientific community. In pursuit of this goal, we introduced nonmagnetic transition metals to alloy with elemental nickel, and studied the magnetic properties of nickel binary alloys Ni1−xMox and Ni1−yCuy as a function of x and y up to the critical concentrations xcr and ycr at which the FM transition TC disappears. TC−x(y) phase diagrams were constructed via the Arrott–Noakes scaling of magnetization data. An enhanced Sommerfeld coefficient (the value of C/T as T→0) is observed near xcr and ycr, manifesting the effect of quantum fluctuations. However, the spin glass behavior is identified through the ac magnetic susceptibility measurements. This observation rules out the possibility of the existence of the FM QCP in both systems.