Disclosed herein are a modified high cis polydiene polymer, processes for preparing the modified high cis polydiene polymer, and tire rubber compositions containing the modified high cis polydiene polymer. The processes make use of a functionalizing compound of formula I or formula II and a coupling agent to prepare the modified high cis polydiene polymer from a quantity of conjugated diene monomer polymerized using a lanthanide-based catalyst system. The modified high cis polydiene polymer includes at least one polymer chain having a residue from the functionalizing compound and a residue from the coupling agent and can be utilized in tire rubber compositions in combination with other ingredients such as fillers.