Doxorubicin is cytotoxic anthracycline antibiotic drug used in cancer treatment. The drug's efficacy in various kinds of cancer made its usage dominant for treating cancers. In this study, we determined the solubility of the doxorubicin in three different polymers, i.e., poly (N-isopropyl acrylamide), polyethylene glycol, and polyvinyl pyrrolidone, to increase the doxorubicin's drug efficacy on the targeted tumor site. We investigated the doxorubicin-polymer interactions with carbon-nanotube in the aqueous environment for the targeted delivery application using classical molecular dynamics simulations. An in-depth atomistic insight into polymer interaction with the drug/carbon-nanotube/water is obtained within the study. We have critically analyzed various properties such as interaction energy, hydrogen bonds between polymer-drug and polymer-water, the diffusion coefficient of the drug, end-to-end distance, radius of gyration of the polymer chains, and finally, drug density contours for different drug to polymer ratios. Our results explain the selection of effective monomer chain length of polymer and the suitability of the polymer carrier with doxorubicin.