We have studied the magnetic excitations in Ca2-xSrxRuO4, x=0.52 and 0.62, which exhibit an anomalously high susceptibility and heavy mass Fermi liquid behavior. Our inelastic neutron scattering experiments reveal strongly enhanced magnetic fluctuations around an incommensurate wave-vector (0.22,0,0) pointing to a magnetic instability. The magnetic fluctuations show no correlation in the c direction and also along the RuO2 planes the signal is extremely broad, Deltaq=0.45 A(-1). These fluctuations can quantitatively account for the high specific heat coefficient and relate to the high macroscopic susceptibility. The magnetic scattering is attributed to the d(xy) band, the active band for spin triplet superconductivity in Sr2RuO4.