In this work, we have investigated the Cabibbo-suppressed process ${\Lambda }_c\to {\pi }^0\eta p$, by taking into account the intermediate scalar state $a_0\left(980\right)$, which could be dynamically generated from the S-wave pseudoscalar-pseudoscalar interaction within the chiral unitary approach. We have calculated the ${\pi }^0\eta$ invariant mass distribution, and found that there is a significant structure associated to the $a_0\left(980\right)$. We have also roughly estimated the branching fraction $B({\Lambda }_c\to {\pi }^0\eta p)\sim {10}^{-4}$. We encourage our experimental colleagues to measure the process ${\Lambda }_c\to {\pi }^0\eta p$ for searching for the state $a_0\left(980\right)$ in this reaction.