Scalable quantum computing architectures increasingly rely on multi-core designs, where qubits are distributed across multiple processing cores interconnected through a quantum Network-on-Chip (NoC). In such systems, inter-core communication is typically realized through entanglement-assisted quantum teleportation, making efficient entanglement generation critical for performance. In this paper, we perform a comparative study of three entanglement management paradigms for multi-core quantum processors: reactive on-demand generation (ODG), proactive continuous pre-generation (CGP), and an adaptive continuous pre-generation approach (ACGP). While ODG generates entanglement only when required, CGP reduces average teleportation latency by pre-generating EPR pairs in the background. To improve upon this, we propose ACGP which dynamically adjusts entanglement generation probabilities based on observed inter-core communication patterns. We evaluate these approaches using an extended SeQUeNCe simulator on mesh-based multi-core architectures on real benchmark circuits. Results show that ACGP significantly reduces average teleportation latency compared to ODG and CGP. Although pre-generation introduces fidelity degradation due to storage time, entanglement purification effectively restores fidelity with minimal impact on latency. These results demonstrate that adaptive entanglement managements can substantially improve communication efficiency in scalable quantum multi-core systems.