The efficient delivery of drugs to cells depends on their diffusion through the extracellular matrix (ECM) of tissues. Here we present a study on the diffusion of nanoprobes of radius from 1 nm to over 100 nm in the ECM of spheroids of three cell types (HeLa, MCF-7 and fibroblasts). We quantified the nanoparticle transport in the spheroids' proliferating zone. We determined the size-dependent viscosity of the ECM. We revealed that nanoobjects up to 10 nm in radius exhibited unobstructed diffusion in the ECM, regardless of the spheroid type. The presented length-scale dependent viscosity profiles for spheroids pave the way for advanced modelling of drug administration through tissues.