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Axion-like particles (ALPs) are predicted in some well-motivated theoriesbeyond the Standard Model. The TeV gamma-rays from active galactic nuclei (AGN)suffer attenuation by the pair production interactions with the cosmicbackground light (EBL/CMB) during its travel to the earth. The attenuation canbe circumvented through photon-ALP conversions in the AGN and Galaxymagnetic-field, and a flux enhancement is expected to arise in the observedspectrum. In this work, we study the potential of the AGN gamma-ray spectrumfor energy up to above 100\,TeV to probe ALP-parameter space at around $\mu$eV,where the coupling $g_{a\gamma}$ is so far relatively weakly constrained.  We find the nearby and bright sources, Mrk\,501, IC\,310 and M\,87, aresuitable for our objective. Assuming an intrinsic spectrum exponential cutoffenergy, we extrapolate the observed spectra of these sources up to above100\,TeV by the models with/without ALPs. For $g_{a\gamma}\gtrsim2\times$$10^{-11} \rm GeV^{-1}$ with $m_{a}\lesssim0.5\,\mu$eV, the flux ataround 100\,TeV predicted by the ALP model can be enhanced more than an orderof magnitude than that from the standard absorption, and could be detected byLHAASO. Our result is subject to the uncertainty from the intrinsic cutoffenergy and the AGN lobe (or plume) magnetic-field. For an optimisticestimation, the constraint can be improved to $g_{a\gamma}\gtrsim2\times$$10^{-11} \rm GeV^{-1}$ with $m_{a}\lesssim1\,\mu$eV. This requirefurther observations on these sources by the forthcoming CTA, LHAASO, SWGO andso on.

Probing $\mu$eV ALPs with future LHAASO observation of AGN $\gamma$-ray spectra