Fluctuation dynamos are thought to play an essential role in magnetized galaxy evolution, saturating within $sim0.01~$Gyr and thus potentially acting as seeds for large-scale dynamos. However, unambiguous observational confirmation of the fluctuation dynamo action in a galactic environment is still missing. This is because, in spiral galaxies, it is difficult to differentiate between small-scale magnetic fields generated by a fluctuation dynamo and those due to the tangling of the large-scale field. We propose that observations of magnetic fields in elliptical galaxies would directly probe the fluctuation dynamo action. This is motivated by the fact that in ellipticals, due to their lack of significant rotation, the conventional large-scale dynamo is absent and the fluctuation dynamo is responsible for controlling the magnetic field strength and structure. By considering turbulence injected by Type Ia supernova explosions and possible magnetic field amplification by cooling flows, we estimate expected magnetic field strengths of $0.2~-~1 ,mu{rm G}$ in quiescent elliptical galaxies. We use a semi-analytic model of galaxy formation to estimate the distribution and redshift evolution of field strengths, tentatively finding a decrease in magnetic field strength with decreasing redshift. We analyse a sample of radio sources that exhibit the Laing-Garrington (LG) effect (radio polarization asymmetry in jets) and infer magnetic field strengths between $0.14~-~1.33 ,mu{rm G}$ for a uniform thermal electron density and between $1.36~-~6.21,mu{rm G}$ for the thermal electron density following the King profile. We examine observational techniques for measuring the magnetic field saturation state in elliptical galaxies, focusing on Faraday RM grids, the LG effect, synchrotron emission, and gravitational lensing, finding appealing prospects for future empirical analysis.
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