We report a molecular dynamics study of the transport coefficients and the infinite frequency shear modulus of liquid iron at high temperatures and high pressures. We observe a simultaneous rise of both the shear viscosity and the diffusion coefficient along the melting line and estimate whether liquid iron can vitrify under Earth-core conditions. We show that in the conditions of the model studied in our work iron demonstrates a moderate increase of viscosity along the melting line. It is also demonstrated that at the limit of high temperatures and high pressures the liquid iron behaves similarly to the soft sphere system with exponent n ≈ 4.6.