We explore if the star zet02 Ret, which belongs to a binary system, is in (or going to) a state similar to the MM. To do so, we have collected more than 430 spectra acquired between 2000 and 2019 with the HARPS, REOSC, UVES, and FEROS spectrographs. We performed a detailed long-term activity study of both components using the Mount Wilson index, which is obtained from the Ca II H&K lines. To search for signs of an activity cycle, we analyzed the resulting time-series with the Generalized Lomb-Scargle and CLEAN periodograms. Our spectroscopic analysis shows a high activity level for zet01 Ret and a significant decrease in the magnetic activity cycle amplitude of zet02 Ret. By analogy with the scenario that proposes a weak solar cycle during the MM, we suggest that activity signatures showed by zet02 Ret, i.e., a very low activity level when compared to its stellar companion, a notably decreasing amplitude (~47%), and a cyclic behaviour, are possible evidence that this star could be in a MM state. It is, to our knowledge, the first MM candidate star detected through a highly discrepant activity behaviour in a binary system.