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Recent studies have revealed a notable timing feature in several black hole X-ray binaries (BHXBs) during the soft-to-hard transition at the outburst decay. Within a narrow frequency range, the phase lags between high- and low-energy X-ray light curves exhibit a sudden increase, accompanied by a drop in the coherence function. These narrow features have been associated with a quasi-periodic oscillation (QPO) appearing only in the imaginary part of the cross spectrum (CS). This QPO remains undetected in the power density spectrum (PDS) and is known as imaginary QPO. Motivated by these results, we analyse five years of NICER observations of the BHXB AT2019wey during its low-hard state (LHS) and hard-intermediate state (HIMS). We find an imaginary QPO in the CS of AT2019wey, with similar characteristics as those found in other BHXBs, making AT2019wey the fifth BHXB in which such QPOs have been found. As the source hardens, the frequency of the imaginary QPO drops from ~5 Hz to ~1 Hz, while its phase lag rises from ~0.3 rad to ~0.7 rad during the HIMS and from ~0.5 rad to ~0.6 rad during the LHS. During the HIMS, the phase-lag energy spectrum of the imaginary QPO shows a typical U-shaped profile, while the shape changes in the LHS. The rms spectrum of the imaginary QPO rises below ~2 keV, peaks at around ~2 keV and decreases at higher energies, which may be associated with the presence of a relatively cool corona. We compare the properties of the imaginary QPO with those of the type-B and C QPOs in BHXBs and find a tentative connection to type-C QPOs. Combining the imaginary QPOs detected in AT2019wey with those reported in other sources, we find a systematic increase of QPO phase lags with QPO frequency. However, we cannot conclude whether the phase lags of imaginary QPOs exhibit the inclination dependence previously observed in type-C QPOs.