We report electron spin resonance (ESR) results for the heavy fermion metal YbRh2(Si1-xGex)2(x=0.05)YbRh2(Si1-xGex)2(x=0.05), where Ge doping suppresses the antiferromagnetic (AFM) ordering and thus brings the system very close to a AFM quantum critical point. The well-defined properties of the ESR signal demonstrate its origin from the Kondo ion Yb3+Yb3+ itself. A comparison with previous ESR results on the Ge-undoped compound stresses the need for a ESR-consistent local moment screening temperature close to zero. Our results are consistent with the localized moment scenario of quantum criticality