We study the momentum and temperature dependencies of magnetic susceptibilities and magnetic exchange in paramagnetic fcc iron by a combination of density functional theory and supercell dynamical mean-field theory (DFT+DMFT). We find that in agreement with experimental results the antiferromagnetic correlations with the wave vector close to (0,0,2π) dominate at low temperatures (as was also obtained previously theoretically), while the antiferromagnetic and ferromagnetic correlations closely compete at the temperatures T∼1000 K, where γ-iron exists in nature. Inverse staggered susceptibility has linear temperature dependence at low temperatures, with negative Weiss temperature θstagg≈-340 K; the inverse local susceptibility is also linear at not too low temperatures, showing well formed local moments. Analysis of magnetic exchange shows that the dominant contribution comes from first two coordination spheres. In agreement with the analysis of the susceptibility, the nearest-neighbor exchange is found to be antiferromagnetic at low temperatures, while at temperature of the α-γ structural phase transition its absolute value becomes small, and the system appears on the boundary between the regimes with strongest antiferro- and ferromagnetic correlations.