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Context. It is well known that from 1645 to 1715 solar activity was notablylow and the number of sunspots was extremely reduced. This epoch is known asthe Maunder Minimum (MM). The study of stars in prolonged activity minima likethe MM could help to shed light on this enigmatic epoch.  Aims. To explore if the star $\zeta^{2}$ Ret, which belongs to a binarysystem, is in a state similar to the MM. We have collected more than 430spectra acquired between 2000 and 2019 with the HARPS, REOSC, UVES, and FEROSspectrographs.  Methods. We performed a detailed long-term activity study of both componentsusing the Mount Wilson index, which is obtained from the Ca II H\&K lines. Tosearch for signs of an activity cycle, we analyzed the resulting time-serieswith the Generalized Lomb-Scargle and CLEAN periodograms.  Results. Our spectroscopic analysis shows a high activity level for zet01 Retand a significant decrease in the magnetic activity cycle amplitude of$\zeta^{2}$ Ret. Thus, the activity difference between both components has beenslightly increased ($\Delta$log (RHK) $\sim$0.24 dex), when compared to thepreviously reported value. The long series analyzed here allowed us torecalculate and constrain the period of $\zeta^{2}$ Ret to $\sim$7.9 yr. Wealso detected a long-term activity cycle of $\sim$4.2 yr in $\zeta^{1}$ Ret.  Conclusions. By analogy with the scenario that proposes a weak solar cycleduring the MM, we suggest that activity signatures showed by $\zeta^{2}$ Ret,i.e., a very low activity level when compared to its stellar companion, anotably decreasing amplitude ($\sim$47%), and a cyclic behaviour, are possibleevidence that this star could be in a MM state. It is, to our knowledge, thefirst MM candidate star detected through a highly discrepant activity behaviourin a binary system.

Detecting prolonged activity minima in binary stars. The case of $\zeta^{2}$ Ret