Defects in the rutile $\mathrm{Ti}{\mathrm{O}}_{2}$ structures have been extensively studied, but the intrinsic defects of the oxygen-deficient ${\mathrm{Ti}}_{n}{\mathrm{O}}_{2n\ensuremath{-}1}$ phases have not been given the same amount of consideration. Those structures, known as Magn\'eli phases, are characterized by the presence of ordered planes of oxygen vacancies, also known as shear planes, and it has been shown that they form conducting channels inside TiO-based memristor devices. Memristors are excellent candidates for a new generation of memory devices in the electronics industry. In this paper we present density-functional-theory--based electronic structure calculations for ${\mathrm{Ti}}_{n}{\mathrm{O}}_{2n\ensuremath{-}1}$ Magn\'eli structures using $\text{PBESol}+U$ ($0\ensuremath{\le}U\ensuremath{\le}5$ eV) and Heyd-Scuseria-Ernzerhof functionals, showing that intrinsic defects present in these structures are responsible for the appearance of states inside the band gap, which can act as intrinsic dopants for the enhanced conductivity of $\mathrm{Ti}{\mathrm{O}}_{2}$ memristive devices.