The magnetic excitations in FeSe are studied from first principles applying linear response density functional theory. The position of the selenide layer is varied to model the transition between paramagnetic and antiferromagnetic phases. In the paramagnetic phase, close to the magnetic instability, we find a branch of long-lived collective spin excitations (paramagnons). An estimation of the paramagnon-mediated effective electron-electron interaction supports the scenario of Cooper pairing in FeSe induced by spin fluctuations.