A nematic transition preceding a long-range spin density wave antiferromagnetic phase is a common feature of many Fe based superconductors. However, in the FeSe system with a nematic transition at $T_{rm s} approx$ 90 K no evidence for long-range static magnetism down to very low temperature was found. The lack of magnetism is a challenge for the theoretical description of FeSe. Here, we investigated high-quality single crystals of FeSe using high-field (up to 9.5 Tesla) muon spin rotation ($mu$SR) measurements. The $mu$SR Knight shift and the bulk susceptibility linearly scale at high temperatures but deviate from this behavior around $T^{*} sim 10$ K, where the Knight shift exhibits a kink. This behavior hints to an essential change of the electronic and/or magnetic properties crossing the region near $T^{*}$. In the temperature range $T_{rm s} gtrsim T gtrsim T^{*}$ the muon spin depolarization rate follows a critical behavior $Lambda propto T^{-0.4}$. The observed non-Fermi liquid behavior with a cutoff at $T^{*}$ indicates that FeSe is in the vicinity to a antiferromagnetic quantum critical point. Our analysis is suggestive for $T^{*}$ triggered by the Lifshitz transition.
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