With its information-theoretic security, quantum-key-distribution-enabled optical networks (QKD-ON) have become a promising candidate for future optical networks. The concept of quantum key pool (QKP) was introduced to offer an effective strategy for storing quantum keys. However, with the loss on its theoretical security due to storing these keys, balancing the storage of quantum keys and the security requirements of QKD-ONs poses a major challenge in their practical deployments. Hence, in this paper a concept of quasi-real-time key provisioning (QRT-KP) is introduced to address the tradeoff between quantum key storage and the degree of security. To satisfy the practical deployment of QRT-KP and the requirement of high-traffic flow, we propose a multi-path based QRT-KP (MP-QRT-KP) algorithm. Simulation results show that the MP-QRT-KP effectively enhances the performance of QKD-ONs in different scenarios, and it turns out that the algorithm performs better than single-path based QRT-KP (SP-QRT-KP) in terms of the success probability of key-allocation requests and key-resources utilization.