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In present work, we investigated $K^{-}+\, ^{3}\mathrm{He}$ reaction at lowenergies. The coupled-channel Faddeev AGS equations were solved for$\bar{K}Nd-\pi\Sigma{d}$ three-body system in momentum representation toextract the scattering amplitudes. To trace the signature of the$\Lambda$(1405) resonance in the $\pi\Sigma$ invariant mass, the deuteronenergy spectrum for $K^{-}+\,^{3}\mathrm{He}\rightarrow\pi\Sigma{d}$ reactionwas obtained. Different types of $\bar{K}N-\pi\Sigma$ potentials based onphenomenological and chiral SU(3) approaches were used. As a remarkable resultof this investigation, it was found that the deuteron energy spectrum,reflecting the $\Lambda$(1405) mass distribution and width, depends quitesensitively on the $\bar{K}N-\pi\Sigma$ model of interaction. Hence accuratemeasurements of the $\pi\Sigma$ mass distribution have the potential todiscriminate between possible mechanisms at work in the formation of the$\Lambda$(1405).

Trace of $\Lambda(1405)$ resonance in low energy $K^{-}+\, ^{3}\mathrm{He}\rightarrow (\pi^{0}\Sigma^{0})+d$ reaction