Context. Planets form in circumstellar disks around pre-main-sequence stars. A key question is, how do the formation and evolution of protoplanetary disks depend on stellar mass? Studies of circumstellar disks at infrared and submillimeter wavelengths around intermediate-mass Herbig Ae/Be stars have revealed disk structures such as cavities, gaps, and spiral arms. The Herbig Ae/Be stars represent an older population of intermediate-mass pre-main-sequence stars. Since these evolve toward the main sequence on timescales comparable to those of typical disk dissipation, a full picture of disk dispersal in intermediate-mass pre-main-sequence stars must include the intermediate-mass T Tauri (IMTT) stars. Aims. We seek to find the precursors of the Herbig Ae/Be stars in the solar vicinity within 500 pc from the Sun. We do this by creating an optically selected sample of IMTT stars from the literature, here defined as stars of masses 1.5 M_⊙≤ M_*≤ 5 M_⊙ and with a spectral type between F and K3. Methods. We used literature optical photometry (0.4–1.25 μm) and distances determined from Gaia DR2 parallax measurements together with Kurucz stellar model spectra to place the stars in a HR diagram. We employed Siess evolutionary tracks to identify IMTT stars from the literature and derived masses and ages. We used Spitzer spectra to classify the disks around the stars into Meeus Group I and Group II disks based on their [F₃₀/F_13.5] spectral index. We also examined the 10 μm silicate dust grain emission and identified emission from polycyclic aromatic hydrocarbons (PAH). From this, we built a qualitative picture of the disks around the IMTT stars and compared this with available spatially resolved images at infrared and submillimeter wavelengths to confirm our classification. Results. We find 49 IMTT stars with infrared excess. The identified disks are similar to the older Herbig Ae/Be stars in disk geometries and silicate dust grain population. The detection frequency of PAHs is higher than from disks around lower mass T Tauri stars but less frequent than from Herbig Ae/Be disks. Spatially resolved images at infrared and submillimeter wavelengths suggest gaps, and spirals are also present around the younger precursors to the Herbig Ae/Be stars. Conclusions. Comparing the timescale of stellar evolution toward the main sequence and current models of protoplanetary disk evolution, the similarity between Herbig Ae/Be stars and the IMTT stars points toward an evolution of Group I and Group II disks that are disconnected and represent two different evolutionary paths.