We investigate the imaginary part of the wave vector dependent dynamic spin susceptibility in Sr$_2$(Ru$_{0.99}$Ti$_{0.01}$)O$_4$ as a function of temperature using neutron scattering. At T=5 K, two-dimensional incommensurate (IC) magnetic fluctuations are clearly observed around $mathbf{Q}_text{c}=(0.3,0.3,L)$ up to approximately 60 meV energy transfer. We find that the IC excitations disperse to ridges around the $(pi,pi)$ point. Below 50 K, the energy and temperature dependent excitations are well described by the phenomenological response function for a Fermi liquid system with a characteristic energy of 4.0(1) meV. Although the wave vector dependence of the IC magnetic fluctuations in Sr$_2$(Ru$_{0.99}$Ti$_{0.01}$)O$_4$ is similar to that in the Fermi liquid state of the parent compound, Sr$_2$RuO$_4$, the magnetic fluctuations are clearly suppressed by the Ti-doping.
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