We report the results of the deepest Galactic plane (|b|<17.5{deg}) survey in the 67.9 and 78.4keV nuclear de-excitation lines of titanium-44 (^44^Ti) performed using the data acquired with the IBIS/ISGRI instrument onboard the INTEGRAL satellite during 12yr of operation. The peak sensitivity of our survey reached an unprecedented level of 4.8x10^-6^ph/cm2/s (3{sigma}) that improves the sensitivity of the survey done by Compton Gamma-Ray Observatory/COMPTEL by a factor of ~5. As a result, constraining upper limits for all sources from the catalogue of Galactic supernova remnants (SNRs; Green, 2014, Cat. VII/272) are derived. These upper limits can be used to estimate the exposure needed to detect ^44^Ti emission from any known SNR using existing and prospective X- and gamma-ray telescopes. Among the youngest Galactic SNRs, only Cas A shows significant ^44^Ti emission flux in good agreement with the NuSTAR measurements. We did not detect any other sources of titanium emission in the Galactic plane at significance level higher than 5{sigma} confirming previous claims of the rarity of such ^44^Ti-producing SNRs.