The impact of cosmic reionization on the Ly𝛼 forest power spectrum has recently been shown to be significant even at low redshifts (𝑧 ∼ 2). This memory of reionization survives cosmological time scales because high-entropy mean-density gas is heated to ∼ 3 × 10 4 K by reionization, which is inhomogeneous, and subsequent shocks from denser regions. In the near future, the first measurements of the Ly𝛼 forest 3D power spectrum will be very likely achieved by upcoming observational efforts such as the Dark Energy Spectroscopic Instrument (DESI). In addition to abundant cosmological information, these observations have the potential to extract the astrophysics of reionization from the Ly𝛼 forest. We forecast, for the first time, the accuracy with which the measurements of Ly𝛼 forest 3D power spectrum can place constraints on the reionization parameters with DESI. Specifically, we demonstrate that the constraints on the ionization efficiency, 𝜁, and the threshold mass for haloes that host ionizing sources, 𝑚 turn , will have the 1𝜎 error at the level of 𝜁 = 25.0 ± 11.9 and log 10 (𝑚 turn /M ) = 8.7 +0.35 −0.70 , respectively. The Ly𝛼 forest 3D power spectrum will thus provide an independent, probably even earlier in detection with DESI, probe of reionization with a sensitivity only slightly worse than the upcoming 21 cm power spectrum measurement with the Hydrogen Epoch of Reionization Array (HERA).