The neutron capture cross section of ²⁴¹Am is an important quantity for nuclear energy production and fuel cycle scenarios. Several measurements have been performed in recent years with the aim to reduce existing uncertainties in evaluated data. Two previous measurements, performed at the 185 m flight-path station EAR1 of the neutron time-of-flight facility n_TOF at CERN, have permitted to substantially extend the resolved resonance region, but suffered in the near-thermal energy range from the unfavorable signal-to-background ratio resulting from the combination of the high radioactivity of ²⁴¹Am and the rather low thermal neutron flux. The here presented ²⁴¹Am(n,γ) measurement, performed with C₆D₆ liquid scintillator gamma detectors at the 20 m flight-path station EAR2 of the n_TOF facility, took advantage of the much higher neutron flux. The current status of the analysis of the data, focussed on the low-energy region, will be described here.