The interactions of heavy quarks with the partonic environment at finite temperature and finite quark chemical potential are investigated in terms of transport coefficients within the dynamical quasiparticle model (DQPM) designed to reproduce the lattice-QCD (lQCD) results (including the partonic equation of state) in thermodynamic equilibrium. These results are confronted with those of nuclear many-body calculations close to the critical temperature . The hadronic and partonic spatial diffusion coefficients join smoothly and show a pronounced minimum around at as well as at finite . Close to and above its absolute value matches the lQCD calculations for . The smooth transition of the heavy-quark transport coefficients from the hadronic to the partonic medium corresponds to a crossover in line with lattice calculations, and differs substantially from perturbative-QCD calculations which show a large discontinuity at . This indicates that in the vicinity of dynamically dressed massive partons should be the effective degrees of freedom in the quark-gluon plasma.