Plasmas with negative triangularity (NT) shape have been recently shown to be able to achieve H-mode levels of confinement in L-mode, avoiding detrimental edge localised modes. Therefore, this plasma geometry is now studied as a possible viable option for a future fusion reactor. Within this framework, an NT option is under investigation for the full power scenario of the Divertor Tokamak Test (DTT) facility, under construction in Italy, with delta top=-0.32/delta bottom similar or equal to 0.02 top/bottom triangularity values at the separatrix. The transport properties of this scenario are studied in this work. Gyrokinetic GENE simulations and integrated modelling using ASTRA with the quasi-linear trapped gyro-Landau fluid (TGLF) model have been performed. The emerging picture from the ASTRA-TGLF runs with boundary conditions at rho tor=0.94 is that, in the L-mode NT option, the larger peaking of the kinetic profiles in the edge region is not sufficient to recover the loss of the PT H-mode pedestal, and reach similar central temperature values. Two additional shapes are also considered, obtained by flipping the triangularity of the scenarios, to single out the effect of the triangularity sign. A negligible 'direct' effect of the triangularity is found for the L-mode, while a small beneficial effect is observed for the H-mode. The ASTRA-TGLF results are validated by GENE and TGLF stand-alone at two selected radii. GENE shows ITG dominant micro-instability and explains the small beneficial effect of the NT for the H-mode as due to a strong reduction of the heat fluxes, when reversing the triangularity, with a relatively high Ti stiffness. An improvement of the predicted performances of the NT DTT scenario could come from rho tor greater than or similar to 0.9 , as indicated by some recent experiments at the tokamak a configuration variable (TCV) and ASDEX Upgrade.