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We investigate, using a systematic computational approach, the possibility of the existence of two-dimensional quasicrystalline phases of binary metal-oxides. Our approach relies on the construction of the complete two-dimensional binary phase diagram through the use of unbiased global structural prediction methods. We then identify, in the low-energy periodic phases, structural elements that can be used to generate quasicrystalline phases through an inflation process. In this way we obtain chemically consistent two-dimensional quasicrystal approximants of both barium and titanium oxides. In the proposed structures, the metallic sites occupy the vertices of the aperiodic square-triangle tiling, while the oxygen atoms decorate the interior of the polygons. We then study the properties of the approximants, both free-standing and deposited on a metallic substrate. Finally, we discuss in which circumstances the formation of these phases seems to be favored.