This depends on the polymer where you want to embed the Al2O3 nanoparticles. In any case, you can functionalize the NPs with a large numbers of compounds to mix NPs with polymers homogeneously.
1. You could try a coupling agent such as a (meth)acrylic-functionalized organophosphonic acid. Organophosphonic acids react with alumina particles rapidly (so simply mixing the alumina and phosphonate in solvent is fine), but you will need to use quite a bit due to the high surface area of nanoparticles. There are methacrylic and acrylic-functional silanes/siloxanes out there as well, however be warned that they suffer from poor hydrolytic stability on alumina.
2. Try ethylene acrylic acid copolymer - this is heavily used as an adhesive layer in metallized foil packaging to improve adhesion between the aluminum layer and polyethylene, polypropylene, PET and so on.