We report localization of lipid membrane microdomains to specific "poles" of asymmetric giant vesicles (GVs) in response to local internal composition. Interior aqueous microdomains were generated in a simple model cytoplasm composed of a poly(ethyleneglycol) (PEG)/dextran aqueous two-phase system (ATPS) encapsulated in the vesicles. The GV membrane composition used here was a modification of a DOPC/DPPC/cholesterol mixture known to form micrometer-scale liquid ordered and liquid disordered domains; we added lipids with PEG 2000 Da-modified headgroups. Osmotically induced budding of the ATPS-containing GVs led to structures where the PEG-rich and dextran-rich interior aqueous phases were in contact with different regions of the vesicle membrane. Liquid ordered (L-o) membrane domains rich in PEG-terminated lipids preferentially coated the PEG-rich aqueous phase vesicle "body", while coexisting liquid disordered (L-d) membrane domains coated the dextran-rich aqueous phase "bud". Membrane domain positioning resulted from interactions between lipid headgroups and the interior aqueous polymer solutions, e.g., PEGylated headgroups with PEG and dextran polymers. Heating resulted first in patchy membranes where L. and Ld domains no longer showed any preference for coating the PEG-rich vs dextran-rich interior aqueous volumes, and eventually complete lipid mixing. Upon cooling lipid domains again coated their preferred interior aqueous microvolume. This work shows that nonspecific interactions between interior aqueous contents and the membrane that encapsulates them can drive local chemical heterogeneity, and offers a primitive experimental model for membrane and cytoplasmic polarity in biological cells.