  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.
