Functionalization of polymers is an attractive approach to introduce specific molecular forces that can enhance drug–polymer interaction to achieve higher drug loading when used as drug delivery systems. The novel amphiphilic block copolymer of methoxy poly(ethylene glycol) and poly(jasmine lactone) i.e., mPEG-b-PJL, derived from renewable jasmine lactone provides free allyl groups on the backbone thus, allowing flexible and facile post-synthesis functionalization. In this study, mPEG-b-PJL and its carboxyl functionalized polymer mPEG-b-PJL-COOH were utilised to explore the effect of ionic interactions on the drug–polymer behaviour. Various drugs with different pKa values were employed to prepare drug-loaded polymeric micelles (PMs) of mPEG-b-PJL, mPEG-b-PJL-COOH and Soluplus® (polyvinyl caprolactam–polyvinyl acetate–polyethylene glycol graft copolymer) via a nanoprecipitation method. Electrostatic interactions between the COOH pendant on mPEG-b-PJL-COOH and the basic drugs were shown to influence the entrapment efficiency. Additionally, molecular dynamics (MD) simulations were employed to understand the polymer–drug interactions at the molecular level and how polymer functionalization influenced these interactions. The release kinetics of the anti-cancer drug sunitinib from mPEG-b-PJL and mPEG-b-PJL-COOH was assessed, and it demonstrated a sustainable drug release pattern, which depended on both pH and temperature. Furthermore, the cytotoxicity of sunitinib-loaded micelles on cancer cells was evaluated. The drug-loaded micelles exhibited dose-dependent toxicity. Also, haemolysis capacity of these polymers was investigated. In summary, polymer functionalization seems a promising approach to overcome challenges that hinder the application of polymer-based drug delivery systems such as low drug loading degree.